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SECTION - A

1. Fill in the blanks:

(i) For the digital in figure, the expression for the output f is _________

(ii) In interleaved memory organization, consecutive words are stored in

consecutive memory modules in ________ interleaving, whereas consecutive words are stored within the module in ________ interleaving.

(iii) Consider the number given by the decimal expression:

3 216 * 9 16 *7 16 *5 3+ + +

The number of 1’s in the unsigned binary representation of the number is

________.

(iv) Using the 8087 arithmetic coprocessor with the 8087 CPU requires that the

8087 CPU is operated ________.

(v) When two 4-bit binary number 3 2 1 0 3 2 1 0

and A a a a a B b b b b= = are multiplied,

the digit 1c of the product C is given by _________

(vi) Consider the following PASCAL program segment:

if i mode 2 = 0 then

while i > = 0 do

begin

i:=i div 2;

if i mod 2 < > 0 do then i:=i – 1

else i:=i – 2

end

An appropriate loop-invariant for the while-loop is ______

(vii) The minimum number of comparisons required to sort 5 elements is _____

a b

x

y

f





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(viii) The weighted external path length of the binary tree in figure is _____

(ix) If the binary tree in figure is traversed in inorder, then the order in which the

nodes will be visited is ______

(x) Consider the following recursive definition of fib:

fib (n) : = if n = 0 then 1

else if n = 1 than 1

else fib (n – 1) + fib ( n – 2)

The number of times fib is called (including the first call) for an evaluation of

fib (7) is ___________

(xi) The arithmetic expression : ( ) * / **a b c d e f+ − is to be evaluated on a two-

address machine, where each operands, the number of registers required to

evaluate this expression is ______. The number of memory access of operand is __________.

(xii) A given set of processes can be implemented by using only

parbegin/parend statement, if the precedence graph of these processes is ________

(xiii) The number of integer-triples (i.j.k) with 1 ≤ i.j.k ≤ 300 such that i + j + k is

divisible by 3 is ________

(xiv) If the longest chain in a partial order is of length n then the partial order

can be written as a ______ of n antichains.

(xv) The maximum number of possible edges in an undirected graph with a

vertices and k components is ________.

15

9 10

7 5

4 2

1

4 6

7

3

5

2

8





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2. Match the pairs in the following questions by writing the corresponding letters only.

(i)

(A) IEEE 488 (P) specifies the interface for connecting a single device

(B) IEEE 796 (Q) specifies the bus standard for connecting a computer to other

devices including CPU’s

(C) IEEE 696 (R) specifies the standard for an instrumentation bus

(D) RS232-C (S) specifies the bus standard for the “backplane” bus called multibus.

(ii) For the 8086 microprocessor:

(iii)

(A) Buddy system (P) Run-time type specification

(B) Interpretation (Q) Segmentation

(C) Pointer type (R) Memory allocation

(D) Virtual memory (S) Garbage collection

(iv)

(A) The number distinct binary trees with n nodes (P)

!

2

n

(B) The number of binary strings of length of 2n with an equal number of 0’s and 1’s (Q)

3n

n

(C) The number of even permutations of n objects (R)

2n

n

(D) The number of binary strings of length 6m which are palindromes with 2n 0’s.

(S)

1 2

1

n

n n

+

(A) RQ/GT (P) Used by processor for holding the bus for consecutive instruction cycles.

(B) LOCK (Q) Used for extending the memory or I/O cycle times

(C) HOLD (R) Used for getting hold of processor bus in minimum bus mode

(D) READY (S) Used for requesting processor bus in minimum bus mode.





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3. Choose the correct alternatives (more than one may be correct) and write the corresponding letters only:

(i) The advantages of CMOS technology over a MOS is:

(a) lower power dissipation

(b) greater speed

(c) smaller chip size

(d) fewer masks for fabrication

(e) none of the above

(ii) Advantage of synchronous sequential circuits over asynchronous ones is:

(a) faster operation

(b) ease of avoiding problems due to hazards

(c) lower hardware requirement

(d) better noise immunity


(iii) The total size of address space is a virtual memory systems is limited by

(a) the length of MAR

(b) the available secondary storage

(c) the available main memory

(d) all of the above


(iv) The TRAP interrupt mechanism of the 8085 microprocessor:

(a) executes an instruction supplied by an external device through the INTA

signal

(b) executes an instruction from memory location 20H

(c) executes a NOP

(d) none of the above

(v) The ALE line of an 8085 microprocessor is used to:

(a) latch the output of an I/O instruction into an external latch

(b) deactivate the chip-select signal from memory devices

(c) latch the 8 bits of address lines AD7-AD0 into an external latch

(d) find the interrupt enable status of the TRAP interrupt

(e) None of the above





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(vi) Kruskal’s algorithm for finding a minimum spanning tree of a weighted graph G with vertices and m edges has the time complexity of:

(a) ( )2O n

(b) ( )O mn

(c) ( )O m n+

(d) ( )logO m n

(e) ( )2O m

(vii) The following sequence of operations is performed on a stack:

PUSH (10), PUSH (20), POP, PUSH (10), PUSH (20), POP, POP, POP,

PUSH (20), POP

The sequence of values popped out is:

(a) 20, 10, 20, 10, 20

(b) 20, 20, 10, 10, 20

(c) 10, 20, 20, 10, 20

(d) 20, 20, 10, 20, 10

(viii) Consider the following Pascal function:

function X (M:integer) : integer;

var i:integer;

begin

i = 0;

while i*i<M do i; =i+1

X;=i

end

The function call X(N), if N is positive, will return

(a) ( )N

(b) ( ) 1N +

(c) N

(d) 1N +


(ix) A “link editor” is a program that:

(a) matches the parameters of the macro-definition with locations of the

parameters of the macro call





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(b) matches external names of one program with their location in other programs

(c) matches the parameters of subroutine definition with the location of

parameters of subroutine call.

(d) acts as link between text editor and the user

(e) acts as a link between compiler and user program.

(x) Indicate all the true statements from the following:

(a) Recursive descent parsing cannot be used for grammar with left recursion.

(b) The intermediate form the representing expressions which is best suited for

code optimization is the post fix form.

(c) A programming language not supporting either recursion or pointer type

does not need the support of dynamic memory allocation.

(d) Although C does not support call by name parameter passing, the effect can

be correctly simulated in C.

(e) No feature of Pascal violates strong typing in Pascal.

(xi) Indicate all the false statements from the statements given below:

(a) The amount of virtual memory available is limited by the availability of

secondary storage.

(b) Any implementation of a critical section requires the use of an indivisible

machine-instruction, such as test-and-set.

(c) The LRU page replacement policy may cause hashing for some type of

programs.

(d) The best fit techniques for memory allocation ensures the memory will never be fragmented.

(xii) If1 2 3, and F F F are propositional formulae such that

1 2 3 1 1 2 and ~F F F F F F∧ → ∧ → are both tautologies, then which of the

following is true:

(a) Both 1 2 and F F are tautologies

(b) The conjunction 1 2F F∧ is not satisfiable

(c) Neither is tautologous

(d) Neither is satisfiable


(xiii) Let ( )1 1 0 *, 11*0 and t 1*0r s= + = = be three regular expressions. Which

one of the following is true?

(a) ( ) ( ) ( ) ( ) and L s L r L s L t⊆ ⊆

(b) ( ) ( ) ( ) ( ) and L r L s L s L t⊆ ⊆





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(c) ( ) ( ) ( ) ( ) and L s L t L s L r⊆ ⊆

(d) ( ) ( ) ( ) ( ) and L t L s L s L r⊆ ⊆


(xiv)Which one of the following is the strongest correct statement about a finite

language over some finite alphabet ?∑

(a) It could be undecidable

(b) It is Turing-machine recognizable

(c) It is a context-sensitive language

(d) It is a regular language


4. Give short answers to the following questions:

(i) Convert the following Pascal statement to a single assignment statement:

if x > 5 they y:=true

else y:=false;

(ii) Convert the Pascal statement repeat S until B; into an equivalent Pascal

statement that uses the while construct.

(iii) Obtain the optimal binary search tree with equal probabilities for the

identifier set ( ) ( )1 2 3, , if, stop,whilea a a =

(iv) If a finite axiom system A for a theory is complete and consistent, then is

every subsystem of A complete and consistent? Explain briefly.

SECTION – B

5. (a) Analyse the circuit in figure and complete the following table:

a b nQ

0 0

0 1

1 0

1 1

Q

a

b





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(b) Find the minimum sum of products form of the logic function.

( ) ( ) ( ), , , 0,2,8,10,15 3,11,12,14f A B C D m d= +∑ ∑

Where m and d denote the min-terms and don’t cares respectively.

(c) Find the maximum clock frequency at which the counter in figure, can be

operated. Assume that the propagation delay through each flip-flop and AND

gate is 10 ns. Also assume that the setup time for the JK inputs of the flip-flops is negligible.

6. (a) Using D flip-flop and gates, design a parallel-in/serial-out shift register that shifts data from left to right with the following input lines:

(i) Clock CLK

(ii) Three parallel data inputs A, B, c

(iii) Serial input S

(iv) Control input load / SHIFT .

(b) Design a 1024 bit serial-in/serial-out unidirectional shift register using a 1K ×

1 bit RAM with data input ,in

D data output out

D and control input

READ/WRITE . You may assume that availability of standard SSI and MSI components such as gates, registers and counters.

7. It is required to design a hardwired controller to handle the fetch cycle of a single

address of an indexed instruction should be derived in the fetch cycle itself.

Assume that the lower order 8 bits of an instruction constitute the operand field.

(a) Give the register transfer sequence for realizing the above instruction fetch

cycle.

(b) Draw the logic schematic of the hardwired controller including the date path.

8. (a) Consider an 8085 based system operating with the following specification:

Crystal frequency : 6 MHz

ROM map : 0000 through 07FF

J0 Q0 K0 CK

J1 Q1

K1 CK

J2 Q2

K2 CK

Clock

1





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PORT-DATE OUTPUT

WROF PORT 40 H

INTERRUPT

BUFFULL

STROBE INPUT FROM DEVICE

RAM map : 1000 through 17 FF:

ROM requires one wait state.

RAM requires no wait state.

Determine the instruction cycle time for each of the following instructions:

(i) ORI A, 22

(ii) DCR M

Assume the following initial conditions of the CPU registers (in hex) for each

of the instructions:

A = 55, B = AA, C = F7, D = 10, H = 10, L = FF, PC = 0200, SP = 17FO.

(b) Developing an output port interface (draw a block schematic) for an 8085

based system with a demultiplexed address bus which incorporates a

handshake protocol as per the timing diagram given in figure. The interface

should include a status input port at I/O address 40H which reads the

INTERRUPT and BUFFFULL signals through the most significant bit and the

least significant bit, respectively. The output data port is at the same I/O

address 40H and is activated by a write operation. Assume the availability of SSI and MSI level components only.

Write a short program segment which performs a 200 H byte programmed

I/O data transfer to the device from memory address 3400 H,

9. (a) Consider the following pseudo-code

(all data items are of type integer):

Procedure P (a, b, c);

a:=2;

c:=a+b;

end P

begin

x:=1

y:=5;





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z:=100;

P(x,x*y,z);

Write (‘x=’,x,z=’,z)

end:

Determine its output, if the parameters are passed to the procedure P by (i)

value, (ii) reference and (iii) name.

(b) For the following pseudo-code, indicate the output, if

(i) static scope rules and (ii) dynamic scope rules are used

Var, a, b : inteer;

Procedure P;

a:=5; b:=10

end P;

procedure Q;

var a, b : integer;

P;

end Q;

begin

a:=1; b:=2;

Q;

Write (‘a =’, a, ‘b=’,b)

end.

10. Consider the following grammar for arithmetic expression using binary operators

– and/which are not associative:

( )

E E T T

TT

F F

F E id

→ −

→

→

(E is the start symbol)

(a) Is this grammar unambiguous? If so, what is the relative precedence

between – and/if not, give an unambiguous grammar that gives/precedence over -

(b) Does the grammar allow expressions with redundant parentheses as in

(id/id) or in id-(id/id)? If so, convert the grammar into one which does not

generate expressions with redundant parentheses. Do this with minimum

number of changes to the given production rules and adding at most one more production rule.





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11. Consider the following scheme for implementing a critical section in a situation with three processes and .j kP P

;iP

repeat

flag [i]:=true;

while flag [j] or flag [k] do

case turn of

j : if flag [j] then

begin

flag [i]:=false;

while turn ≠ i do skip;

flag [i] : true

end;

k : if flag [k] then

begin

flag [i]:=false,

while turn ≠ i do skip;

flag [i]:=true

end

end

critical section

if turn = i then turn:=j;

flag [i]:=false

non-critical section

until false;

(a) Does the scheme ensure mutual exclusion in the critical section? Briefly

explain.

(b) Is there a situation in which a waiting process can never enter the critical

section? If so, explain and suggest modifications to the code to solve this problem.

12. Suppose, a database consists of the following relations:

SUPPLIER (SCODE, SNAME, CITY)

PART (PCODE, PNAME, PDESC, CITY)

PROJECTS (PRCODE, PRNAME, CITY)

SPRR (SCODE, PCODE, PRCODE, QJY)





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(a) Write SQL programs corresponding to the following queries:

(i) Print PCODE value for parts supplied to any project in DELHI by a supplier

in DELHI.

(ii) Print all triples (CITY, PCODE, CITY), such that a supplier in the first city

supplies the specified part to a project in the second city, but do not print triples in which the two CITY values are the same.

(b) Write algebraic solutions to the following:

(i) Get SCODE values for suppliers who supply to both projects PR1 and PR2.

(ii) Get PRCODE values for projects supplied by at least one supplier not in

the same city.

13. Give an optimal algorithm is pseudo-code for sorting a sequence of n numbers

which has only k distinct numbers (k is not known a Priori. Give a brief analysis for the time-complexity of your algorithm).

14. Consider the binary tree in Figure:

(a) What structure is represented by the binary tree?

(b) Give the different steps for deleting the node with key 5 so that the structure

is preserved.

(c) Outline a procedure in pseudo-code to delete an arbitrary node from such a

binary tree with n nodes that preserves the structure. What is the worst-case

time-complexity of your procedure?

15. (a) Show that the product of the least common multiple and the greatest

common divisor of two positive integers a and b is a*b.

(b) Consider the following first order formula:

( ) ( ) ( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( ) ( )( )

( ) ( )

, , ~ ,

, , ,

~ ,

Ax Ey R x y Ax Ay R x y R y x

Ax Ay Az R x y R y z R x z

Ax R x x

∧ →

∧ ∧ →

∧

5

7 13

1

18

20

25

27

11 9 15 17





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(A-universal quantifier and E-existential quantifier)

Does it have finite models?

Is it satisfiable? Is so, give a countable model for it.

16.

(a) Find the number of binary strings w of length 2n with an equal number os 1’s

and 0’s, and the property that every prefix and w has atleast as many 0’s as 1’s.

(b) Show that all vertices in an undirected finite graph cannot have distinct

degrees, if the graph has at least two vertices.

17. (a) Show that Turing machines, which have a read only input tape and constant

size work tape, recognize preasely the class or regular languages.

(b) Let L be the language of all binary strings in which the third symbol from the

right is 1.a Give a non-deterministic finite automaton that recognizes L. How

many states does the minimized equivalent deterministic finite automaton have? Justify your answer briefly?





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SECTION – A


(i) The Boolean function in sum of products form where K-map is given below

(figure) is:___________

(ii) Consider a 3-bit error detection and 1-bit error correction hamming code for

4-bit date. The extra parity bits required would be ________ and the 3-bit

error detection is possible because the code has a minimum distance of ________

(iii) Many microprocessors have a specified lower limit on clock frequency (apart

from the maximum clock frequency limit) because ______

(iv) Many of the advanced microprocessors prefetch instructions and store it in

an instruction buffer to speed up processing. This speed up is achieved because _________

(v) A simple and reliable data transfer can be accomplished by using the

‘handshake protocol’. It accomplishes reliable data transfer because for every data item sent by the transmitter __________.

(vi) In an 11-bit computer instruction format, the size of address field is 4-bits.

The computer uses expanding OP code technique and has 5 two-address

instructions and 32 two-address instructions and the number of zero-address instructions it can support is _________

(vii) Macro expansion is done in pass one instead of pass two in a pass macro

assembler because _________

(viii) The purpose of instruction location counter in an assembler is _______

(ix) Complexity of Kruskal’s algorithm for finding the minimum spanning tree of

an undirected graph containing n vertices and m edges if the edges are sorted is __________

(x) Maximum number of edges in a planar graph with n vertices is ________

2. Choose the correct alternatives (more than one may be correct) and write the

corresponding letters only:

(i) The operation which is commutative but not associative is:

(a) AND (b) OR (c) EX-OR (d) NAND

(ii) All digital circuits can be realized using only

(a) Ex-OR gates (b) Multiplexers

(c) Half adders (d) OR gates

0

A

0 1

0

1

B C

1

A





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(iii) Bit-slice processors

(a) Can be cascaded to get any desired word length processor

(b) speed of operation is independent of the word length configured

(c) don’t contain anything equivalent of program counter in a ‘normal’

microprocessor

(d) contain only the data path of a ‘normal’ CPU

(iv) PCHL is an instruction in 8085 which transfers the contents of the register

pair HL to PC. This is not a very commonly used instruction as it changes the

flow of control in rather ‘unstructured’ fashion. This instruction can be useful

in implementing.

(a) if ……. then ….. else ….. construct (b) while …… construct

(c) case …… construct (d) call …… construct

(v) Start and stop bits do not contain an ‘information’ but are used in serial communication for

(a) Error detection (b) Error correction

(c) Synchronization

(d) Slowing down the communications

(vi) Which of the following problems is not NP-hard?

(a) Hamiltonian circuit problem

(b) The 0/1 Knapsack problem

(c) Finding bi-connected components of a graph

(d) The graph colouring problem

(vii) A 2-3 tree is tree such that

(a) all internal nodes have either 2 or 3 children

(b) all paths from root to the leaves have the same length

The number of internal nodes of a 2-3 tree having 9 leaves could be

(a) 4 (b) 5 (c) 6 (d) 7

(viii) A non-planar graph with minimum number of vertices has

(a) 9 edges, 6 vertices (b) 6 edges, 4 vertices

(c) 10 edges, 5 vertices (d) 9 edges, 5 vertices

(ix) Following algorithm(s) can be used to sort n integers in the range 31 n K in

0 (n) time

(a) Heapsort (b) Quicksort (c) Mergesort (d) Radixsort





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(x) At a particular time of computation the value of a counting semaphore is 7.

Then 20 P operations and 15 V operations were completed on this

semaphore. The resulting value of the semaphore is:

(a) 42 (b) 2 (c) 7 (d) 12

(xi) A computer system has 6 tape drives, with n process completing for them.

Each process may need 3 tape drives. The maximum value of n for which the system is guaranteed to be deadlock free is:

(a) 2 (b) 3 (c) 4 (d) 1

(xii) Which of the following is an example of a spooled device?

(a) The terminal used to the input data for a program being executed.

(b) The secondary memory device in a virtual memory system

(c) A line printer used to print the output of a number of jobs.

(d) None of the above

(xiii) For a context-free grammar, FOLLOW(A) is the set of terminals that can

appear immediately to the right of non-terminal A in some “sentential” form.

We define two sets LFOLLOW(A) and RFOLLOW(A) by replacing the word

“sentential” by “left sentential” and “right most sentential” respectively in the

definition of FOLLOW(A).

Which of the following statements is/are true?

(a) FOLLOW(A) and FOLLOW (A) may be different.

(b) FOLLOW(A) and FOLLOW (A) are always the same.

(c) All the three sets are identical.

(d) All the three sets are different.

(xiv) Consider the SLR(1) and LALR (1) parsing tables for a context free

grammar. Which of the following statements is/are true?

(a) The go to part of both tables may be different.

(b) The shift entries are identical in both the tables.

(c) The reduce entries in the tables may be different.

(d) The error entries in the tables may be different.

(xv) Which of the following predicate calculus statements is/are valid:

(a) ( ) ( ) ( ) ( ) ( ) ( ) ( ) x P x x Q x x P x Q x∀ ∨ ∀ → ∀ ∨

(b) ( ) ( ) ( ) ( ) ( ) ( ) ( ) x P x x Q x x P x Q x∃ ∧ ∃ → ∃ ∧

(c) ( ) ( ) ( ) ( ) ( ) ( ) ( )x P x Q x x P x x Q x∀ ∨ → ∀ ∨ ∀

(d) ( ) ( ) ( ) ( ) ( ) ( ) ( )~x P x Q x x P x x Q x∃ ∨ → ∀ ∨ ∃





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(xvi) Which of the following is/are tautology

(a) a b b c∨ → ∧ (b) a b b c∧ → ∨

(c) ( )a b b c∨ → → (d) ( )a b b c→ → →

(xvii) Which of the following regular expression identifies are true?

(a) ( )* *r r= (b) ( ) ( )* * *r s r s= +

(c) ( )* * *r s r s+ = + (d) * * * *r s r s= +

(xviii) If G is a context-free grammar and w is a string of length l in L(G), how long is a derivation of w in G, if G is Chomsky normal form?

(a) 2l (b) 2l + 1 (c) 2l - 1 (d) l

(xix) Context-free languages are

(a) closed under union (b) closed under complementation

(c) closed under intersection (d) closed under Kleene closure

(xx) In which of the cases stated below is the following statement true?

“For every non-deterministic machine 1M there exists an equivalent

deterministic machine 2M recognizing the same language“.

(a) 1M is non-deterministic finite automaton

(b) 1M is a non-deterministic PDA

(c) 1M is a non-deterministic Turing machine

(d) For no machine 1M use the above statement true

3. Write short answers to the following:

(i) Which of the following macros can put a macro assembler into an infinite loop?

.MACRI M1,X .MACRO M2, X

..IF EQ,X .IF EQ, X

M1 X+1 M2X

.ENDC .ENDC

.IF NE, X .IF NE, X

WORD X .WORD X + 1

.ENDC .ENDC

.ENDM .ENDM

Give an example of a call that does so.

(ii) Mention the pass number for each of the following activities that occur in a

two pass assembler





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(a) object code generation (b) literals added literal table

(c) listing printed

(d) address resolution of local symbols

(iii) How many edges are there in a forest with p components having n vertices in

all?

(iv) Assume that the last element of the set is used as partition element in

Quicksort. If n distinct elements from the set [1…..n] are to be sorted, give an input for which Quicksort takes maximum time.

(v) Which page replacement policy sometimes leads to more page faults when

size of memory is increased?

SECTION – B

4. (a) Consider addition in two’s complement arithmetic. A carry from the most

significant but does not always correspond to an overflow. Explain what is the condition for overflow in two’s complement arithmetic.

(b) A priority encoder accepts three input signals (A, B and C) and produce a

two-bit output ( )1 0,X X corresponding to the highest priority active input

signal. Assume A has the highest priority followed by B and C has the lowest

priority. If none of the inputs are active the output should be 00. design the priority encoder using 4:1 multiplexers as the main components.

(c) Design a 3-bit counter using D-flip flops such that not more than one flip-flop

changes state between any two consecutive states.

5. (a) The access times of the main memory and the Cache memory, in a computer

system, are 500 n sec and 50 n sec, respectively. It is estimated that 80% of

the main memory request are for read the rest for write. The hit ratio for the

read access only is 0.9 and a write-through policy (where both main and

cache memories are updated simultaneously) is used. Determine the average time of the main memory.

(b) Three devices A, B and C are corrected to the bus of a computer,

input/output transfers for all three devices use interrupt control. Three

interrupt request lines INTR1, INTR2 and INTR3 are available with priority of INTR1 > priority of INTR2 > priority of INTR3.

Draw a schematic of the priority logic, using an interrupt mask register, in

which Priority of A > Priority of B > Priority of C.

6. A microprocessor is capable of addressing 1 megabyte of memory with a 20-bit

address bus. The system to be designed requires 256 K bytes of RAM, 256 K

bytes of EPROM, 16 I/O devices (memory mapped I/O) and 1 K byte of EERAM (electrically erasable RAM).





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(a) Design a memory map (to reduce decoding logic) and show the decoding

logic if the components available are:

Type Size Speed

RAM 6 K × 8 140 n sec

EPROM 256 K × 8 150 n sec

EERAM 256 × 8 500 n sec-read 3µsec-write

(b) The micro processor is operating at 12.5 mHz and provides time equivalent

to two clock cycles for memory read and write. Assuming control signals similar to 8085, design the extra logic required for interfacing EERAM.

7. Consider the function F(n) for which the pseudo code is given below:

Function F(n)

begin

F1 1

if(n=1) then F 3

else For i = 1 to n do

begin

C 0

For j = 1 to F(n – 1) do

begin C C + 1 end

F1 = F1 * C

end

F = F1

end

[n is a positive integer greater than zero]

(a) Derive a recurrence relation for F(n)

(b) Solve the recurrence relation for a closed form solutions of F(n).

8. Let T be a Depth First Tree of a undirected graph G. An array P indexed by

vertices of G is given. P[V] is the parent of vertex V, in T. Parent of the root is the root itself.

Give a method for finding and printing the cycle formed if the edge (u,v) of G not

in T (i.e., e G T∈ − ) is now added to T.

Time taken by your method must be proportional to the length of the cycle.

Describe the algorithm in a PASCAL – like language. Assume that the variables

have been suitably declared.

9. Suggest a data structure for representing a subnet S of integers from 1 to n.

following operations on the set S are to be performed in constant time (independent of cardinality of S).





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(i) MEMBER (X): Check whether X is the set S or not

(ii) FIND-ONE(S): If S is not empty, return one element of the set S (any

arbitrary element will do)

(iii) ADD (X): Add integer x to set S

(iv) DELETE(X): Delete integer x from S.

Give pictorial examples of your data structure. Give routines for these operations

in an English like language. You may assume that the data structure has been suitably initialized. Clearly state your assumptions regarding initialization.

10. (a) What type of parameter passing mechanism (call-by-value, call-by-reference,

call-by-name, or-by-value result) is the following sequence of actions truing

to implement for a procedure call P (A[i]) where P (i:integer) is a procedure and A is an integer array?

1. Create a new local variable, say z.

2. Assign to z the value of A[i].

3. Execute the body of P using z for A[i]

4. Set A[i] to z.

Is the implementation correct? Explain and correct it if necessary. You are

supposed to make only small changes.

(b) Show the activation records and the display structure just after the

procedures called at lines marked x and y have started their execution. Be sure to indicate which of the two procedures named A you are referring to.

Program Test;

Procedure A;

Procedure B;

Procedure A;

……

end a;

begin

y:A;

end B;

begin

B;

end A;

begin

x:A;

end Test.





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11. (a) Write syntax directed definitions (semantic rules) for the following grammar

to add the type of each identifier to its entry in the symbol table during

semantic analysis. Rewriting the grammar is not permitted and semantic rules are to be added to the ends of productions only.

D TL;

T int

T real

L L, id

L id

(b) Write 3-address intermediate code (quadruples) for the following boolean

expression in the sequence as it would be generated by a compiler. Partial

evaluation of Boolean expressions is not permitted. Assume the usual rules

of precedence of the operators.

(a + b) > (c + d) or a > c and b < d

12. (a) Draw the precedence graph for the concurrent program given below:

S1

parbegin

begin

S2:S4

end;

begin

S3;

parbegin

S5;

begin

S6:S8

End

parend

end;

S7

Parend;

S9

(b) Let the page reference and the working set window be c c d b c e c e a d and

4, respectively. The initial working set at time t = 0 contains the pages a, d,

e, where a was referenced at time t = 0, d was referenced at time t = -1,

and e was referend at time t = -2. determine the total number of page faults

and the average number of page frames used by computing the working set

at each reference.





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13. (a) How is redundancy reduced in the following models?

(i) Hierarchical

(ii) Network

(iii) Relational

Write a one line answer in each case.

(b) Suppose we have a database consisting of the following three relations:

FREQUENTS (CUSTOMER, HOTEL)

SERVES (HOTEL, SNACKS)

LIKES (CUSTOMER, SNACKS)

The first indicates the hotels each customer visits, the second tells which snacks

each hotel serves and the last indicates which snacks are liked by each customer.

Express the following query in relational algebra: print the hotels that serve a snack that customer Rama likes.

14. (a) If G is a group of even order, then show that there exists an element ,a e≠

the identity in g, such that 2a e=

(b) Consider the set of integers 1,2,3,4,6,8,12,24 together with the two binary

operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent?

(i) group (ii) ring

(iii) field (iv) lattice

15. (a) Uses Modus ponens ( ),A A B→ = or resolution to show that the following set

is inconsistent:

(1) ( ) ( ) ( )~Q x P x V R a→

(2) ( ) ( )~R a Q a

(3) ( )Q a

(4) ( )~ P y

Where x and y are universally quantified variables, a is a constant and P, Q, R

are monadic predicates.

(b) Let S be the set of all integers and let n > 1 be a fixed integer. Define for a,

b ,S∈ a R biff a-b is a multiple of n. Show that R is an equivalence relation

and finds its equivalence classes for n = 5.

16. Which of the following three statements are true? Prove your answer.

(i) The union of two recursive languages is recursive.

(ii) The language is a primeO n′′ is not regular.

(iii) Regular languages are closed under infinite union.





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SECTION - A

1. In questions 1.1 to 1.7 below, one or more of the alternatives are correct. Write

the code letter(s) a, b, c, d corresponding to the correct alternative(s) in the

answer book. Marks will be given only if all the correct alternatives have been

selected and no incorrect alternative is picked up.

1.1 The eigen vector(s) of the matrix

( )

0 0

0 0 0 , 0 is are

0 0 0

α

α

≠

(a) ( )0,0,α (b) ( ),0,0α (c) ( )0,0,1 (d) ( )0, ,0α

1.2 The differential equation

2

2sin 0

d y dyy

dxdx+ + = is:

(a) linear (b) non-linear (c) homogeneous (d) of degree two

1.3 Simpson’s rule for integration gives exact result when ( )f x is a polynomial of

degree

(a) 1 (b) 2 (c) 3 (d) 4

1.4 Which of the following is (are) valid FORTRAN 77 statement(s)?

(a) DO 13 I = 1 (b) A = DIM ***7

(c) READ = 15.0 (d) GO TO 3 = 10

1.5 Fourier series of the periodic function (period 2π) defined by

( )0,

is, 0

p xf x

x x p

− < <=

< <

( )2

1 1cos 1 cos cos sin

4

pn nx n nx

nnπ π

π

+ − −

∑

But putting x = π, we get the sum of the series.

2 2 2

1 1 11 is

3 5 7+ + + + K

(a) 2

4

π (b)

2

6

π (c)

2

8

π (d)

2

12

π

1.6 Which of the following improper integrals is (are) convergent?





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(a) 1

0

sin

1 cos

xdxx−∫ (b)

0

cos

1

xdx

x

∞

+∫ (c) 20 1

xdx

x

∞

+∫ (d)

1

50

1 cos

2

xdx

x

−∫

1.7 The function ( ) 2, 3 2 hasf x y x y xy y x= − + +

(a) no local extremum

(b) one local minimum but no local maximum

(c) one local maximum but no local minimum

(d) one local minimum and one local maximum

2. In questions 2.1 to 2.10 below, each blank ( _____) is to be suitably filled in. In

the answer book write the question number and the answer only. Do not copy the question. Also, no explanations for the answers are to be given.

2.1 ( ) ( )

( )0

1 2 cos 1lim is _______

1 cos

x

x

x e x

x x→

− + −

−

2.2 The radius of convergence of the power series

( )

( )3

3

3 !

!

mm

xm

∞

∑ is: ______________

2.3 If the linear velocity Vuris given by

$ 2 2 ,V x yi xyz j yz k= + −ur

The angular velocity ωurat the point (1, 1, -1) is ________

2.4 Given the differential equation, y x y′ = − with the initial condition ( )0 0y = . The

value of ( )0.1y calculated numerically upto the third place of decimal by the

second order Runga-Kutta method with step size h = 0.1 is ________

2.5 For X = 4.0, the value of I in the FORTRAN 77 statement

5.0 * 31 2 **2 is _____

*3 4

X

X= − + +

2.6 The value of the double integral 1

1

20 0 is ______

1xxdxdy

y+∫ ∫





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2.7 If

1 0 0 1

0 1 0 1

0 0

0 0 0

Ai i

i

− − = −

the matrix 4,A calculated by the use of Cayley-Hamilton

theorem or otherwise, is _________

2.8 Given $ 2 2 2cos sinzV x yi x e j z yk= + +ur

$ and S the surface of a unit cube with one

corner at the origin and edges parallel to the coordinate axes, the value of integral

$1

. .s V ndS∫ ∫ur

is _______

2.9 The differential equation 0ny y+ = is subjected to the boundary conditions.

( )0 0y = ( ) 0y λ =

In order that the equation has non-trivial solution(s), the general value of λ is

__________

2.10 The Laplace transform of the periodic function ( )f t described by the curve below,

i.e.,

( )( ) ( )sin if 2 1 2 1,2,3,

0 otherwise

t n t n nf t

π π − ≤ ≤ ==

K

is ___________

0 π 2π 3π 4π 5π 6π 7π 8π t

f(t)





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SECTION II – A

INSTRUCTIONS: There are THREE questions in this Section. Question 6 has 8 parts, 7

has 10 parts, and 8 has 7 parts. Each part of a question carries 2 marks. There may be

more than one correct alternative the multiple-choice questions. Credit will be given if only all the correct alternatives have been indicated.

6.

6.1. Identify the logic function performed by the circuit shown in figure.

(a) exclusive OR (b) exclusive NOR (c) NAND

(d) NOR (e) None of the above

6.2. If the state machine described in figure, should have a stable state, the

restriction on the inputs is given by

(a) . 1ab = (b) 1a b+ = (c) 0a b+ = (d) . 1ab =

(e) 1a b+ =

6.3. For the initial state of 000, the function performed by the arrangement of the J-K

flip-flops in figure is:

(a) Shift Register (b) Mod-3 Counter (c) Mod-6 Counter

(d) Mod-2 Counter (e) None of the above

x

y

A

f(x,y)

J Q

K Q

J Q2

K Q

J Q

K Q

Clock





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6.4. Assume that each character code consists of 8 bits. The number of characters

that can be transmitted per second through an asynchronous serial line at 2400

baud rate, and with two stop bits, is

(a) 109 (b) 216 (c) 218 (d) 219

(e) 240

6.5. Convert the following numbers in the given bases into their equivalents in the

desired bases.

(a) ) )2 10

110.101 x=

(b) ) )10

1118 y H=

6.6. A ROM is used to store the Truth table for a binary multiple unit that will multiply

two 4-bit numbers. The size of the ROM (number of words × number of bits) that

is required to accommodate the Truth table is M words × N bits. Write the values

of M and N.

6.7. A certain moving arm disk storage, with one head, has the following

specifications.

Number of tracks/recording surface = 200

Disk rotation speed = 2400 rpm

Track storage capacity = 62,500 bits

The average latency of this device is P msec and the data transfer rate is Q

bits/sec.

Write the value of P and Q.

6.8. The details of an interrupt cycle are shown in figure.

Given that an interrupt input arrives every 1 msec, what is the percentage of the

total time that the CPU devotes for the main program execution.

Arrival of interrupt input

10µ sec

Main program execution

10µ sec 80µ sec

10µ sec

Saving of CPU state

Interrupt Service Execution

Restoration of CPU state

Main program execution





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7. Note: For sub-questions 7.1 to 7.3, refer to the PASCAL program shown below.

Program PARAM (input, output);

var m, n : integer;

procedure P (var, x, y : integer);

var m : integer;

begin

m : = 1;

x : = y + 1

end;

procedure Q (x:integer; vary : integer);

begin

x:=y+1;

end;

begin

m:=0; P(m,m); write (m);

n:=0; Q(n*1,n); write (n)

end

7.1. The value of m, output by the program PARAM is:

(a) 1, because m is a local variable in P

(b) 0, because m is the actual parameter that corresponds to the formal parameter in p

(c) 0, because both x and y are just reference to m, and y has the value 0

(d) 1, because both x and y are just references to m which gets modified in

procedure P


7.2. The value of n, output by the program PARAM is:

(a) 0, because n is the actual parameter corresponding to x in procedure Q.

(b) 0, because n is the actual parameter to y in procedure Q.

(c) 1, because n is the actual parameter corresponding to x in procedure Q.

(d) 1, because n is the actual parameter corresponding to y in procedure Q.


7.3. What is the scope of m declared in the main program?

(a) PARAM, P, Q (b) PARAM, P (c) PARAM, Q

(d) P, Q (e) none of the above





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7.4. What does the following code do?

var a, b : integer;

begin

a:=a+b;

b:=a-b;

a:=a-b

end;

(a) exchanges a and b (b) doubles a and stores in b

(c) doubles b and stores in a (d) leaves a and b unchanged


7.5. For the program segment given below, which of the following are true?

program main (output);

type link = ^data;

data = record

d : real;

n : link

end;

var ptr : link;

begin

new (ptr);

ptr:=nil;

.ptr^.d:=5.2;

write ln(ptr)

end.

(a) The program leads to compile time error

(b) The program leads to run time error

(c) The program outputs 5.2

(d) The program produces error relating to nil pointer dereferencing


7.6. A simple two-pass assembler does the following in the first pass:

(a) It allocates space for the literals.

(b) It computes the total length of the program

(c) It builds the symbol table for the symbols and their values.

(d) It generates code for all the load and store register instructions.

(e) None of the above.





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7.7. A part of the system software, which under all circumstances must reside in the

main memory, is:

(a) text editor (b) assembler (c) linker (d) loader


7.8. The root directory of a disk should be placed

(a) at a fixed address in main memory (b) at a fixed location on the disk

(c) anywhere on the disk

(d) at a fixed location on the system disk (e) anywhere on the system disk

7.9. Consider a system having m resources of the same type. These resources are

shared by 3 processes A, B and C, which have peak demands of 3, 4 and 6 respectively. For what value of m deadlock will not occur?

(a) 7 (b) 9 (c) 10 (d) 13

(e) 15

7.10. Assume that the following jobs are to be executed on a single processor system

Job Id CPU Burst time

p

q

r

s

t

4

1

8

1

2

The jobs are assumed to have arrived at time 0+ and in the order p, q, r, s, t.

calculate the departure time (completion time) for job p if scheduling is round robin with time slice 1.

(a) 4 (b) 10 (c) 11 (d) 12


8.

8.1. Consider a simple connected graph G with n vertices and n-edges (n>2). Then,

which of the following statements are true?

(a) G has no cycles.

(b) The graph obtained by removing any edge from G is not connected.

(c) G has at least one cycle.

(d) The graph obtained by removing any two edges from G is not connected.

(e) None of the above.





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8.2. The proposition ( )~P p q∧ ∨ is:

(a) a tautology (b) logically equivalent to p q∧

(c) logically equivalent to p q∨ (d) a contradiction


8.3. Let S be an infinite set and 1,

nS SK be sets such that

1 2.

nS S S S∪ ∪ ∪ =K Then,

(a) at least one of the set iS is a finite set

(b) not more than one of the set iS can be finite

(c) at least one of the sets iS is an infinite set

(d) not more than oen of the sets iS can be infinite


8.4. Let A be a finite set of size n. The number of elements in the power set of

A A× is:

(a) 22n

(b) 2

2n (c) ( )2

2n (d) ( )22n


8.5. The less-than relation, <, on reals is

(a) a partial ordering since it is asymmetric and reflexive

(b) a partial ordering since it is antisymmetric and reflexive

(c) not a partial ordering because it is not asymmetric and not reflexive

(d) not a partial ordering because it is not antisymmetric and reflexive


8.6. Let A and B be sets with cardinalities m and n respectively. The number of one-

one mappings (injections) from A to B, when m < n, is:

(a) nm (b) n mP (c) m nC (d) n mC

(e) m nP

8.7. ( )1

,k n

O n≤ ≤

∑ where ( )O n stands for order n is:

(a) ( )O n (b) ( )2O n (c) ( )3O n (d) ( )23O n

(e) ( )21.5O n





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SECTION II - B

INSTRUCTIONS: There are TEN questions in this section. Each question carries 5 marks. Attempt all questions.

9. Assume that only half adders are available in your laboratory. Show that any

binary Boolean function can be implemented using half adders only.

10. The instruction format of a CPU is:

Mode and RegR together specify the operand. RegR specifies a CPU register and

Mode specifies an addressing mode. In particular, Mode = 2 specifies that ‘the

register RegR contains the address of the operand, after fetching the operand,

the contents of RegR are incremented by 1’.

An instruction at memory location 2000 specifies Mode = 2 and the RegR refers

to program counter (PC).

(a) What is the address of the operand?

(b) Assuming that this is a non-jump instruction, what are the contents of PC

after the execution of this instruction?

11. In the three-level memory hierarchy shown in the following table, ip denotes the

probability that an access request will refer to .iM

Hierarchy Level

( )iM

Access Time

( )it Probability of access

( )ip

Page Transfer time

( )iT

1M

2M

3M

610−

510−

410−

0.99000

0.00998

0.00002

0.001 sec

0.1 sec

--

If a miss occurs at level iM , a page transfer occurs from

1iM

+ to

iM and the

average time required for such a page swap is .iT Calculate the average time

At

required for a processor to read one word from this memory system.

OP CODE MODE RegR

One Memory word





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12. The following Pascal program segments finds the largest number in a two-

dimensional integer array 0 1,0 1A n n− − K K using a single loop. Fill up the

boxes to complete the program and write against , , and A B C D in your

answer book. Assume that max is a variable to store the largest value and i,j are the indices to the array.

begin

max:= A , i:=0,j:=0;

while B do

begin

if A[i,j]>max then max:=A[i,j]

if C then j:=j+1

else begin

j:=0;

i:= D

end

end

end.

13. Consider a singly linked list having n nodes. The data items 1 2, ,

nd d dK are stored

in these n nodes. Let X be a pointer to the j-th node (1≤j≤n) in which dj is stored.

A new data item d stored in node with address Y is t be inserted. Give an

algorithm to insert d into the list to obtain a list having items

1 2 1, , , , , ,j j nd d d d d−

K K in the order without using the header.

14. An ISAM (indexed sequential) file consists of records of size 64 bytes each,

including key field of size 14 bytes. An address of a disk block takes 2 bytes. If

the disk block size is 512 bytes and there are 16 K records, compute the size of

the data and index areas in terms of number of blocks. How many levels of tree

do you have for the index?

15. Consider the recursive algorithm given below:

procedure bubblersort (n);

var i,j: index; temp : item;

begin

for i:=1 to n-1 do

if A[i] > A [i+1] then

begin

temp : A[i];

A[i]:=A[i+1];





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A[i+1]:=temp

end;

bubblesort (n -1 )

end

Let na be the number of times the ‘if…then….’ Statement gets executed when the

algorithm is run with value n. Set up the recurrence relation by defining na in

terms of 1.

na

− Solve for

na .

16. Prove by the principal of mathematical induction that for any binary tree, in

which every non-leaf node has 2 descendants, the number of leaves in the tree is one more than the number of non-leaf nodes.

17. Out of a group of 21 persons, 9 eat vegetables, 10 eat fish and 7 eat eggs : 5

persons eat all three. How many persons eat at least two out the three dishes?

18. Show that proposition C is a logical consequence of the formula

( )( ) ( )~A A B C B A∧ → ∨ ∧ →

Using truth tables.

SECTION: II - C

INSTRUCTIONS: There are TEN questions in this section. Each question carries 5

marks. Attempt any FIVE questions. In case more than five questions are attempted, the

first five answers alone will be evaluated.

19. A control algorithm is implemented by the NAND – gate circuitry given in figure

below, which A and B are state variable implemented by D flip-flops, and P is control input. Develop the state transition table for this controller.

B

B

A

A A

B

P

B

B

P

Clock

A

A

DA

A

DB

B





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20. Given that the following is an 8085 program segment:

(a) Identify the function performed by it, and

(b) List the roles of the registers used and the address referred to by it.

LHLD 5000

MVI B, 5

GET: IN 20

MOV M, A

INX H

DCR B

JNZ GET

21. The following page addresses, in the given sequence, were generated by a

program:

1 2 3 4 1 3 5 2 1 5 4 3 2 3

This program is run on a demand paged virtual memory system, with main

memory size equal to 4 pages. Indicate the page references for which page faults

occurs for the following page replacement algorithms.

(a) LRU

(b) FIFO

Assume that the main memory is empty initially.

22. Write a concurrent program using parbegin-parend and semaphores to represent

the precedence constraints of the statements 1 6 to ,S S as shown in figure below.

For questions 23 and 24:

The following relations are used to store data about students, courses, enrollment

of students in courses and teachers of courses. Attributes for primary key in each relation are marked by ‘*’.

S1

S2 S3

S4 S5

S6





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Students (rollno*, sname, saddr)

courses (cno*, cname)

enroll(rollno*, cno*,grade)

teach(tno*,tname,cao*)

(cno is course number, cname is course name, tno is teacher number, tname is

teacher name, sname is student name, etc.)

23. Write a SQL query for retrieving roll number and name of students who got A

grade in at least one course taught by teacher named Ramesh for the above relational database.

24. For the relational database given above, the following functional dependencies

hold:

rollno sname,sdaddr cno cname

tno tname rollno, cno grade

(a) Is the database in 3rd normal form (3NF)?

(b) If yes, prove that it is in 3 NF. If not, normalize, the relations so that they

are in 3 NF (without proving).

25. A simple Pascal like language has only three statements.

(i) assignment statement e.g. x:=expression

(ii) loop construct e.g. for i:=expression to expression do statement.

(iii) sequencing e.g. begin statement ;…; statement end

(a) Write a context-free grammar (CFG) for statements in the above language.

Assume that expression has already been defined. Do not use optional parentheses and * operator in CFG.

(b) Show the parse tree for the following statement:

for j:=2 to 10 do

begin x:=expr1;

y:=expr2

end

26. A stack is used to pass parameters to procedures in a procedure call.

(a) If a procedure P has two parameters as described in procedure definition:

procedure P (var x :integer; y: integer);

and if P is called by ; P(a,b)

State precisely in a sentence what is pushed on stack for parameters a and

b.

(b) In the generated code for the body of procedure P, how will the addressing of

formal parameters x and y differ?





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27. Draw the state transition of a deterministic finite state automaton which accepts

all strings from the alphabet ,a b , such that no string has 3 consecutive

occurrences of the letter b.

28. Let )( , ,*p q be a semigroup where * .p p q= Show that:

(a) * *p q q p= and

(b) *q q q=





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Read the following instructions carefully:

(i) This question paper consists of two sections: A & B.

(ii) Section A has EIGHT questions. Answer all questions in this section.

(iii) Section B has TWENTY questions. Answer any TEN questions in this section.

(iv) Begin answer for this section on a fresh page.

(v) Answer to questions in each section should appear together in the same

sequence in which they appear in the question paper.

(vi) There will be no negative marking.

Section – A

1. Choose one of the alternatives for the following questions:

1.1 FORTRAN implementation do not permit recursion because

(a) they use static allocation for variables

(b) they use dynamic allocation for variables

(c) stacks are not available on all machines

(d) it is not possible to implement recursion on all machines

1.2 Let A and B be real symmetric matrices of size n n× . Then which one of the

following is true?

(a) 1AA′ = (b) 1A A−= (c) AB = BA (d) ( )AB BA′ =

1.3 Backward Euler method for solving the differential equation ( ),dy

f x ydx

= is

specified by, (choose one of the following).

(a) ( )1 ,n n n ny y hf x y+ = + (b) ( )1 1 1,n n n ny y hf x y+ + += +

(c) ( )1 1 2 ,n n n ny y hf x y+ −= + (d) ( ) ( )1 1 11 ,n n ny h f x y+ + += +

1.4 Let A and B be any two arbitrary events, then, which one of the following is true?

(a) ( ) ( ) ( )P A B P A P B∩ = (b) ( ) ( ) ( )P A B P A P B∪ = +

(c) ( ) ( ) ( )P A B P A B P B= ∩ (d) ( ) ( ) ( )P A B P A P B∪ ≤ +

1.5 An unrestricted use of the “goto” statement is harmful because

(a) it makes it more difficult to verify programs

(b) it increases the running time of the programs

(c) it increases the memory required for the programs

(d) it results in the compiler generating longer machine code





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1.6 The number of distinct simple graphs with upto three nodes is

(a) 15 (b) 10 (c) 7 (d) 9

1.7 The recurrence relation that arises in relation with the complexity of binary

search is:

(a) ( ) , k a constant2

nT n T k

= +

(b) ( ) 2 , k a constant

2

nT n T k

= +

(c) ( ) log2

nT n T n

= +

(d) ( )

2

nT n T n

= +

1.8 The logic expression for the output of the circuit shown in figure below is:

(a) AC BC CD+ +

(b) AC BC CD+ +

(c) ABC CD=

(d) A B B C C D+ +

1.9 The rank of matrix

0 0 3

9 3 5 is:

3 1 1

−

(a) 0 (b) 1 (c) 2 (d) 3

1.10 Some group ( ),G o is known to be abelian. Then, which one of the following is

true for G?

(a) 1 for every g g g G−= ∈ (b) 2 for every g g g G= ∈

(c) ( )2 2 2 for every ,goh g oh g h G= ∈ (d) G is of finite order

1.11 In a compact single dimensional array representation for lower triangular

matrices (i.e all the elements above the diagonal are zero) of size ,n n× non-zero

elements (i.e elements of the lower triangle) of each row are stored one after

another, starting from the first row, the index of the ( ),th

i j element of the lower

triangular matrix in this new representation is:

(a) i j+ (b) 1i j+ − (c) ( )12

i ij

−+ (d)

( )12

j ji

−+

1.12 Generation of intermediate code based on an abstract machine model is useful in

compilers because

(a) it makes implementation of lexical analysis and syntax analysis easier

A

B

C

D





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(b) syntax-directed translations can be written for intermediate code generation

(c) it enhances the portability of the front end of the compiler

(d) it is not possible to generate code for real machines directly from high level language programs

1.13 A memory page containing a heavily used variable that was initialized very early

and is in constant use is removed when

(a) LRU page replacement algorithm is used

(b) FIFO page replacement algorithm is used

(c) LFU page replacement algorithm is used


1.14 Which of the following permutations can be obtained in the output (in the same

order) using a stack assuming that the input is the sequence 1, 2, 3, 4, 5 in that order?

(a) 3, 4, 5, 1, 2 (b) 3, 4, 5, 2, 1 (c) 1, 5, 2, 3, 4 (d) 5, 4, 3, 1, 2

1.15 The number of substrings (of all lengths inclusive) that can be formed from a

character string of length n is

(a) n (b) 2n (c) ( )12

n n − (d)

( )12

n n +

1.16 Which of the following conversions is not possible (algorithmically)?

(a) Regular grammar to context free grammar

(b) Non-deterministic FSA to deterministic FSA

(c) Non-deterministic PDA to deterministic PDA

(d) Non-deterministic Turing machine to deterministic Turing machine

1.17 Linked lists are not suitable data structures of which one of the following problems?

(a) Insertion sort (b) Binary search

(c) Radix sort (d) Polynomial manipulation

1.18 Which of the following features cannot be captured by context-free grammars?

(a) Syntax of if-then-else statements

(b) Syntax of recursive procedures

(c) Whether a variable has been declared before its use

(d) Variable names of arbitrary length





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1.19. Which of the following algorithm design techniques is used in the quicksort algorithm?

(a) Dynamic programming (b) Backtracking

(c) Divide and conquer (d) Greedy method

1.20. In which one of the following cases is it possible to obtain different results for

call-by reference and call-by-name parameter passing methods?

(a) Passing a constant value as a parameter

(b) Passing the address of an array as a parameter

(c) Passing an array element as a parameter

(d) Passing an array following statements is true

1.21. Which one of the following statements is true?

(a) Macro definitions cannot appear within other macro definitions in assembly

language programs

(b) Overlaying is used to run a program which is longer than the address space

of computer

(c) Virtual memory can be used to accommodate a program which is longer than

the address space of a computer

(d) It is not possible to write interrupt service routines in a high level language

1.22. Which one of the following statements is false?

(a) Optimal binary search tree construction can be performed efficiently using

dynamic programming.

(b) Breadth-first search cannot be used to find converted components of a graph

(c) Given the prefix and postfix walks over a binary tree, the binary tree cannot

be uniquely constructed.

(d) Depth-first search can be used to find connected components of a graph.

1.23. Consider the following two functions:

( )

( )

3

1 2

2 3

for 0 10,000

for 10,000

for 0 100

for 100

n ng n

n n

n ng n

n n

≤ ≤=

≥

≤ ≤=

>

Which of the following is true?

(a) ( ) ( )( )1 2 is 0g n g n (b) ( ) ( )31 is 0g n n

(c) ( ) ( )( )2 1 is 0g n g n (d) ( ) ( )2 is 0g n n





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1.24. Consider the following heap (figure) in which blank regions are not in use and

hatched region are in use.

The sequence of requests for blocks of size 300, 25, 125, 50 can be satisfied if

we use

(a) either first fit or best fit policy (any one)

(b) first fit but not best fit policy

(c) best fit but first fit policy



2.1 The number of flip-flops required to construct a binary modulo N counter is

__________

2.2. On the set N of non-negative integers, the binary operation __________ is

associative and non-commutative.

2.3. Amongst the properties reflexivity, symmetry, anti-symmetry, transitivity the

relation R =(x,y) 2N x y∈ ≠ satisfies __________

2.4. The number of subsets 1,2, nK with odd cardinality is __________

2.5. The number of edges in a regular graph of degree d and n vertices is _________

2.6. The probability of an event B is 1.P The probability that events A and B occur

together is 2P while the probability that A and B occur together is

3.P The

probability of the event A in terms of 1 2 3, and P P P is __________

2.7. Consider n-bit (including sign bit) 2’s complement representation of integer

number. The range of integer values, N, that can be represented is __________

≤ N ≤ __________

2.8. Let A, B and C be independent events which occur with probabilities 0.8, 0.5 and

0.3 respectively. The probability of occurrence of at least one of the event is

__________

2.9. The Hasse diagrams of all the lattices with up to four elements are __________

(write all the relevant Hasse diagrams).

Increasing addresses

50 150 300 350 600





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2.10. The regular expression for the language recognized by the finite state automaton

of figure is __________

3. Answer the following questions as indicated.

3.1. State True or False with one line explanation

Multiplexing of address/data lines in 8085 microprocessor reduces the instruction

execution time.


Expanding opcode instruction formats are commonly employed in RISC. (Reduced

Instruction Set Computers) machines.


A FSM (Finite State Machine) can be designed to add two integers of any arbitrary length (arbitrary number of digits).

3.4. Match the following items

(i) Newton-Raphson (a) Integration

(ii) Runge-Kutta (b) Root finding

(iii) Gauss-Seidel (c) Ordinary Differential Equations

(iv) Simpson’s Rule (d) Solutions of Systems of Linear Equations


(i) Backus-Naur form (a) Regular expressions

(ii) Lexical analysis (b) LALR(I) grammars

(iii) YACC (c) LL(I) grammars

(iv) Recursive descent parsing (d) General context-free grammars

A B C

0 1 0

0 1

1





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3.6. State True or False with reason

There is always a decomposition into Boyce-Codd normal form (BCNF) that is

lossless and dependency preserving.

3.7. An instance of a relational scheme R(A, B, C) has distinct values for attribute A.

Can you conclude that A is a candidate key for R?

3.8. Give a relational algebra expression using only the minimum number of operators

from ( ),∪ − which is equivalent to .R S∩

3.9. Every subset of a countable set is countable.

State whether the above statement is true or false with reason.


(i) ECL (a) Unipolar; very high speed difficult to fabricate; good resistance

to radiation

(ii) Ga As (b) Unipolar; low power; modest speed and packing density

(iii) TTL (c) Bipolar; highest speed silicon IC; low packing density

(iv) CMOS

(d) Bipolar, modes packing density, inexpensive

3.11. State True or False with reason

Logical data independence is easier to achieve than physical data independence

3.12. Find the inverse of the matrix

1 0 1

1 1 1

0 1 0

−

3.13. Let p and q be propositions. Using only the truth table decide whether

p q⇔ does not imply p q is true or false.

4. (a) Let * be a Boolean operation defined as * A B AB A B= +

If C = A * B then evaluate and fill in the blanks:

(i) A * A = _______

(ii) C * A = _______

(b) Solve the following boolean equations for the values of A, B and C:

1

0

AB AC

AC B

+ =

+ =





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5. A 3-ary tree is a tree in which every internal node has exactly three children. Use

induction to prove that the number of leaves in a 3-ary tree with n interval nodes

is ( )2 1 3.n − +

6. What function of x, n is computed by this program?

Function what (x, n:integer): integer:

Var

value : integer;

begin

value:=1

if n>0 then

begin

if n mod 2 = 1 then

value:=value*x;

value:=value*what(x*x, n div 2);

end;

what:value

end;

7. An array A contains n integers in locations A[0],A[1], ………………..A[n-1]. It is

required to shift the elements of the array cyclically to the left by K places, where

1≤K≤n-1. An incomplete algorithm for doing this in linear time, without using

another is given below. Complete the algorithm by filling in the blanks. Assume all variables are suitably declared.

min:=n;

i=0;

while _____do

begin

temp:=A[i];

j:=i;

while _____do

begin

A[j]:=_____;

j:=(j+K) mod n;

if j<min then

min:=j;

end;

A[(n+i-K)mod n]:=_____;

i:=____________;

end;





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8. A rooted tree with 12 nodes has its nodes numbered 1 to 12 in pre-order. When

the tree is traversed in post-order, the nodes are visited in the order 3, 5, 4, 2,

7, 8, 6, 10, 11, 12, 9, 1.

Reconstruct the original tree from this information, that is, find the parent of

each node, and show the tree diagrammatically.

SECTION – B

Answer any TEN questions in this section.

9. Following 7 bit single error correcting Hamming coded message is received.

(figure below):

7 6 5 4 3 2 1 bit No.

1 0 0 0 1 1 0

Determine if the message is correct (assuming that at most 1 bit could be

corrupted). If the message contains an error find the bit which is erroneous and gives the correct message.

10. Write a program in 8085 Assembly language to Add two 16-bit unsigned BCD(8-

4-2-1 Binary Coded Decimal) number. Assume the two input operands are in BC

and DE Register pairs. The result should be placed in the register pair BC. (Higher order register in the register pair contains higher order digits of operand)

11. Find the contents of the flip-flop 2 1 0, and Q Q Q in the circuit of figure, after giving

four clock pulses to the clock terminal. Assume 2 1 0

000Q Q Q = initially.

12. (a) Assume that a CPU has only two registers 1 2 and R R and that only the

following instruction is available , ; , for , 1,2i j j i jXOR R R R R R i j← ⊕ =

J Q2

CK K

D Q1 CK

T Q0

CK

0Q

Clock 1

(Four clock pulses given here)





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Using this XOR instruction, find an instruction sequence in order to exchange

the contents of the registers 1 2 and .R R

(b) The line p of the circuit shown in figure has stuck at 1 fault. Determine an

input test to detect the fault.

13. Consider the following relational schema:

COURSES (cno, cname)

STUDENTS (rollno, sname, age, year)

REGISTERED FOR (cno, rollno)

The underlined attributes indicate the primary keys for the relations. The ‘year’

attribute for the STUDENTS relation indicates the year in which the student is currently studying (First year, Second year etc.)

(a) Write a relational algebra query to

Print the roll number of students who have registered for cno 322.

(b) Write a SQL query to

Print the age and year of the youngest student in each year.

14. Consider B+ − tree of order d shown in figure?

(A) B+ − tree of order d contains between d and 2d keys in each node

(a) Draw the resulting B+ − tree after inserted in the figure.

(b) For a B+ − tree of order d with n leaf nodes, the number of nodes accessed

during a search is ( )0 .−

A

B

C

p s-a-1

94-7 B

25 38 69 93

10 15 25 36 39 41 47 69 71 75 83 95 99 101 105





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15. (a) Use the patterns given to prove that

( )1

2

0

2 1n

i

i n−

=

+ =∑

(You are not permitted to employ induction)

1 4 9

etc

(b) Use the result obtained in (a) to prove that

( )

1

1

2

n

i

n ni

=

+=∑

16. Every element a of some ring ( ), ,0R + satisfies the equation aoa = a.

Decide whether or not the ring is commutative.

17. State whether the following statements are True or False with reasons for your

answer:

(a) Coroutine is just another name for a subroutine.

(b) A two pass assembler uses its machine opcode table in the first pass of assembly.

18. State whether the following statements are True or False with reasons for your

answer

(a) A subroutine cannot always be used to replace a macro in an assembly

language program.

(b) A symbol declared as ‘external’ in assembly language is assigned an address

outside the program by the assembler itself.

19. (a) Given a set

there is an x-block of 5's in the decimal expansion of S x π=

(Note: x-block is a maximal block of x successive 5’s)

Which of the following statements is true with respect to S? No reasons need

to be given for the answer.

(i) S is regular

(ii) S is recursively enumerable

(iii) S is not recursively enumerable

(iv) S is recursive

(b) Given that a language L1 is regular and that the language 1 2L L∪ is regular, is

the language 2L always regular? Prove your answer.





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20. A grammar G is in Chomsky-Normal Form (CNF) if all its productions are of the

form A BC or A a, where A, B and C, are non-terminals and a is a terminal.

Suppose G is a CFG in CNF and w is a string in L(G) of length, then how long is a derivation of w in G?

21. Consider the following recursive function:

function fib (1:integer);integer;

begin

if (n=0) or (n=1) then fib:=1

else fib:=fib(n-1) + fib(n-2)

end;

The above function is run on a computer with a stack of 64 bytes. Assuming that

only return address and parameter and passed on the stack, and that an integer

value and an address takes 2 bytes each, estimate the maximum value of n for

which the stack will not overflow. Give reasons for your answer.

22. Consider the program below:

Program main;

var r:integer;

procedure two;

begin write (r) end;

procedure one;

var r:integer;

begin r:=5 two; end

begin r:=2;

two; one; two;

end.

What is printed by the above program if

(i) Static scoping is assumed for all variables;

(ii) Dynamic scoping is assumed for all variables.

Give reasons for your answer.

23. Suppose we have a computer with a single register and only three instructions given below:

LOAD addren ; load register

; from addren

STORE addren ; store register

; at addren

ADD addren ; add register to

; contents of addren

; and place the result

; in the register





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Consider the following grammar:

A id :=E E E T T+ T ( )E id

Write a syntax directed translation to generate code using this grammar for the

computer described above.

24. An independent set in a graph is a subset of vertices such that no two vertices in

the subset are connected by an edge. An incomplete scheme for a greedy algorithm to find a maximum independent set in a tree is given below:

V: Set of all vertices in the tree; I:=φ;

While V ≠ φdo

begin

select a vertex u; ∈ V such that

V:=V – u;

if u is such that

then 1:= I u∪

end;

output(I);

(a) Complete the algorithm by specifying the property of vertex u in each case

(b) What is the time complexity of the algorithm.

25. An array a contains n integers in non-decreasing order, 1 2 .A A A n≤ ≤ ≤ K

Describe, using Pascal like pseudo code, a linear time algorithm to find i, j, such

that A i A j+ = a given integer M, if such i, j exist.

26. A queue Q containing n items and an empty stack S are given. It is required to

transfer all the items from the queue to the stack, so that the item at the front of

queue is on the top of the stack, and the order of all other items is preserved.

Show how this can be done in O(n) time using only a constant amount of

additional storage. Note that the only operations which can be performed on the

queue and stack are Delete, Insert, Push and Pop. Do not assume any implementation of the queue or stack.

27. (a) Draw a precedence graph for the following sequential code. The statements

are numbered from 1 6 to S S

S1 read n

S2 i:=1

S3 if i>n goto next

S4 a(i):=i+1

S5 i:=i+1

S6 next : Write a(i)





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(b) Can this graph be converted to a concurrent program using parbegin-parend

construct only?

28. Consider the resource allocation graph given in the figure.

(a) Find if the system is in a deadlock state.

(b) Otherwise, find a safe sequence.

r1 r2

p2 p1 p0

p3

r3





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SECTION - A

1. This question has 25 parts. Each part carries 1 mark. Choose the correct alternative for each part.

1.1 A single instruction to clear the lower four bits of the accumulator in 8085 assebly language?

(a) XRI OFH (b) ANI FOH (c) XRI FOH (d) ANI OFH

1.2 Which of the following statements is true?

(a) ROM is a Read/Write memory

(b) PC points to the last instruction that was executed

(c) Stack works on the principle of LIFO

(d) All instructions affect the flags

1.3 In a vectored interrupt

(a) the branch address is assigned to a fixed location in memory

(b) the interrupt source supplies the branch information to the processor through an interrupt vector

(c) the branch address is obtained from a register in the processor


1.4 In the following Pascal program segment, what is the value of X after the execution of the program segment?

X:=-10; Y:=20;

If X > Y then if X < 0 then X:=abs(X) else X:=2*X;

(a) 10 (b) -20 (c) -10 (d) None

1.5 Merge sort uses

(a) Divide and conquer strategy (b) Backtracking approach

(c) Heuristic search (d) Greedy approach

1.6 The principle of locality justifies the use of

(a) interrupts (b) DMA

(c) Polling (d) Cache Memory

1.7 In a paged segmented scheme of memory management, the segment table itself must have a page table because

(a) the segment table is often too large to fit in one page

(b) each segment is spread over a number of pages





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(c) segment tables point to page table and not to the physical locations of the segment

(d) the processor’s description base register points to a page table

1.8 Which of the following page replacement algorithms suffers from Belady’s anamoly?

(a) Optimal replacement (b) LRU

(c) FIFO (d) Both (a) and (c)

1.9 In some programming languages, an identifier is permitted to be a letter

following by any number of letters or digits. If L and D denote the sets of letters and digits respectively, which of the following expressions defines an identifier?

(a) ( )L D+

∪ (b) ( )*

L L D∪ (c) ( )*

.LD (d) ( )*

. .L LD

1.10 Consider a grammar with the following productions

S a b b c aB

S S b

S bb ab

S bd b b

→ ∝ ∝

→∝

→∝

∝→

The above grammar is:

(a) Context free (b) Regular

(c) Context sensitive (d) LR(k)

1.11 What are x and y in the following macro definition?

macro Add x,y

Load y

Mul x

Store y

end macro

(a) Variables (b) Identifiers

(c) Actual parameters (d) Formal parameters

1.12 What is the distance of the following code 000000, 010101, 000111, 011001, 111111?

(a) 2 (b) 3 (c) 4 (d) 1

1.13 Which of the following strings can definitely be said to be tokens without looking at the next input character while compiling a Pascal program?

I. begin II. program III. <>





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(a) I (b) II (c) III

(d) All of the above

1.14 A linker is given object modules for a set of programs that were compiled separately. What information need to be included in an object module?

(a) Object code

(b) Relocation bits

(c) Names and locations of all external symbols defined in the object module

(d) Absolute addresses of internal symbols

1.15 Which scheduling policy is most suitable for a time shared operating system?

(a) Shortest Job First (b) Round Robin

(c) First Come First Serve (d) Elevator

1.16 For merging two sorted lists of sizes m and n into a sorted list of size m+n, we required comparisons of

(a) ( )O m (b) ( )O n

(c) ( )O m n+ (d) ( )log logO m n+

1.17 A binary tree T has n leaf nodes. The number of nodes of degree 2 in T is:

(a) 2

log n (b) 1n − (c) n (d) 2n

1.18 The probability that a number selected at random between 100 and 999 (both inclusive) will not contain the digit 7 is:

(a) 16

25 (b)

39

10

(c) 27

75 (d)

18

25

1.19. Let R be a symmetric and transitive relation on a set A. Then

(a) R is reflexive and hence an equivalence relation

(b) R is reflexive and hence a partial order

(c) R is reflexive and hence not an equivalence relation


1.20. The number of elements in he power set ( )P S of the set ( ) ( ) ,1, 2,3S φ= is:

(a) 2 (b) 4 (c) 8






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1.21. In the interval 0,π the equation cosx x= has

(a) No solution (b) Exactly one solution

(c) Exactly two solutions (d) An infinite number of solutions

1.22. If at every point of a certain curve, the slope of the tangent equals 2x

y

− the

curve is

(a) a straight line (b) a parabola

(c) a circle (d) an ellipse

1.23. The value of k for which 2 24 8 0x xy ky− + = does not represent a pair of straight

lines (both passing through the origin) is:

(a) 0 (b) 2 (c) 9 (d) 3

1.24. The rank of the following ( ) ( )1 1n n+ × + matrix, where a is a real number is

2

2

2

1

1

1

n

n

n

a a a

a a a

a a a

L

L

M M M M

M M M M

L

(a) 1 (b) 2 (c) n

(d) Depends on the value of a

1.25 The minimum number of edges in a connected cyclic graph on n vertices is:

(a) n - 1 (b) n (c) n + 1


2. This question has 25 parts. Each part carries 2 Marks. Choose the correct

alternative for each part.

2.1 A sequence of two instructions that multiplies the contents of the DE register pair

by 2 and stores the result in the HL register pair (in 8085 assembly language) is:

(a) XCHG and DAD B (b) XTHL and DAD H

(c) PCHL and DAD D (d) XCHG and DAD H

2.2. The capacity of a memory unit is defined by the number of words multiplied by

the number of bits/word. How many separate address and data lines are needed

for a memory of 4 K × 16?

(a) 10 address, 16 data lines (b) 11 address, 8 data lines





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(c) 12 address, 16 data lines (d) 12 address, 12 data lines

2.3. Assume that X and Y are non-zero positive integers. What does the following

Pascal program segment do?

while X <>Y do

if X > Y then

X:=X – Y

else

Y:=Y – X;

write(X);

(a) Computes the LCM of two numbers

(b) Divides the larger number by the smaller number

(c) Computes the GCD of two numbers


2.4. What is the value of X printed by the following program?

program COMPUTE (input, output);

var

X:integer;

procedure FIND (X:real);

begin

X:=sqrt(X);

end;

begin

X:=2

Find(X)

Writeln(X)

end

(a) 2 (b) 2

(c) Run time error (d) None of the above

2.5. What values of A, B, C and D satisfy the following simultaneous Boolean

equations?

0, ,A AB AB AC AB AC CD CD+ = = + + =

(a) A = 1, B = 0, C = 0, D = 1 (b) A = 1, B = 1, C = 0, D = 0

(c) A = 1, B = 0, C = 1, D = 1 (d) A = 1, B = 0, C = 0, D = 0





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2.6. The sequence …………… is an optimal non-preemptive scheduling sequence for the following jobs which leaves the CPU idle for ……………………. unit(s) of time.

(a) 3,2,1),1 (b) (2,1,3,0 (c) 3,2,1),0 (d) 1,2,3,5

2.7. The address sequence generated by tracing a particular program executing in a

pure demand paging system with 100 records per page with 1 free main memory frame is recorded as follows. What is the number of page faults?

0100, 0200, 0430, 0499, 0510, 0530, 0560, 0120, 0220, 0240, 0260, 0320,

0370

(a) 13 (b) 8 (c) 7 (d) 10

2.8. If the cube roots of unity are 1, ω and ω2, then the roots of the following equation

are ( )3

1 8 0x − + =

(a) -1, 1 + 2ω, 1 + 2ω2 (b) 1, 1 - 2ω, 1 - 2ω2

(c) -1, 1 - 2ω, 1 - 2ω2 (d) -1, 1 + 2ω, -1 + 2ω2

2.9. A language with string manipulation facilities uses the following operations

head(s): first character of a string

tail(s): all but the first character of astring

concat(s1,s2):s1 s2

for the string acbc what will be the output of

concat(head(s), head(tail(tail(s))))

(a) ac (b) bc (c) ab (d) cc

2.10. A shift reduce parser carries out the actions specified within braces immediately

after reducing with the corresponding rule of grammar

print"1"

print"2"

print"3"

S xxW

S y

W Sz

→

→

→

What is the translation of xxxxyzz using the syntax directed translation scheme

described by the above rules?

(a) 23131 (b) 11233 (c) 11231 (d) 33211

Job Arrival time Burst time

1 0.0 9

2 0.6 5

3 1.0 1





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2.11. A variant record in Pascal is defined by

type varirec = record

number : integer;

case (var1,var2) of

var1: (x,y : integer);

var2: (p.q.: real)

end

end

Suppose an array of 100 records was declared on a machine which uses 4 bytes

for an integer and 8 bytes for a real. How much space would the compiler have to

reserve for the array?

(a) 2800 (b) 2400 (c) 2000 (d) 1200

2.12. The number of 1’s in the binary representation of

( )3* 4096 15 *256 5*16 3+ + + are:

(a) 8 (b) 9 (c) 10 (d) 12

2.13. A unit vector perpendicular to both the vectors

2 2 and 1 2a i j k b j k= − + = + − is:

(a) ( )1

3i j k+ + (b) ( )

1

3i j k+ − (c) ( )

1

3i j k− − (d) ( )

1

3i j k+ −

2.14. A bag contains 10 white balls and 15 black balls. Two balls are drawn in

succession. The probability that one of them is black and the other is white is:

(a) 2

3 (b)

4

5 (c)

1

2 (d)

2

1

2.15. The iteration formula to find the square root of a positive real number b using the

Newton Raphson method is

(a) ( )1 3 2k k kx x b x+ = + (b) ( )1 3 2k k b kx x x+ +=

(c) ( )2

1 2k k k kx x x x b+ = − + (d) None of the above

2.16. In a virtual memory system the address space specified by the address lines of

the CUP must be __________ than the physical memory size and _______ than the secondary storage size.

(a) smaller, smaller (b) smaller, larger

(c) larger, smaller (d) larger, larger





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2.17. Let A be the set of all non-singular matrices over real number and let* be the matrix multiplication operation. Then

(a) A is closed under* but < A, *> is not a semigroup

(b) <A, *> is a semigroup but not a monoid

(c) <A, *> is a monoid but not a group

(d) <A, *> is a group but not an abelian group

2.18. The solution of differential equation 3 2 0y y y′′ ′+ + = is of the form

(a) 2

1 2

x xC e C e+ (b) 3

1 2

x xC e C e− + (c) 2

1 2

x xC e C e− −+ (d) 2

1 22x xC e C− −+

2.19. If the proposition p ν¬ ⇒ is true, then the truth value of the proposition

( ) ,pV p q¬ ⇒ where ¬ is negation, ‘V’ is inclusive or and ⇒ is implication, is

(a) true (b) multiple valued

(c) false (d) cannot be determined

2.20. Which of the following definitions below generates the same language as L,

where such that 1 ?n nL x y n= >=

I. E xE y xy→

II. ( )x y x xyy+ +

III. x y+ +

(a) I only (b) I and II (c) II and III (d) II only

2.21. The postfix expression for the infix expression

( )* / *A B C D F D E+ + + is:

(a) AB + CD + *F/D + E* (b) ABCD + *F/DE*++

(c) A *B + CD/F *DE++ (d) A + *BCD/F* DE++

2.22. Which of the following statements is true?

I. As the number of entries in a hash table increases, the number of collisions

increases.

II. Recursive programs are efficient

III. The worst case complexity for Quicksort is ( )2O n

IV. Binary search using a linear linked list is efficient.

(a) I and II (b) II and III (c) I and IV (d) I and III





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2.23. A finite state machine with the following state table has a single input x and a single out z.

present state next state, z

x=1 x=0

A D, 0 B, 0

B B, 1 C, 1

C B, 0 D, 1

D B, 1 C, 0

If the initial state is unknown, then the shortest input sequence to reach the final

state C is:

(a) 01 (b) 10 (c) 101 (d) 110

2.24. Let *0,1 , and 0 1 such that 0n nL R n∑ = = ∑ = > then the languages L R∪ and

R are respectively

(a) regular, regular (b) not regular, regular

(c) regular, not regular (d) not regular, no regular

2.25. A computer system has a 4K word cache organized in block-set-associative

manner with 4 blocks per set, 64 words per block. The number of bits in the SET and WORD fields of the main memory address format is:

(a) 15, 40 (b) 6, 4 (c) 7, 2 (d) 4, 6

3. Consider the following high level program segment. Give the contents of the

memory locations for variables W, X, Y and Z after the execution of the program

segment. The values of the variables A and B are 5 CH and 92H, respectively. Also indicate error conditions if any.

var

A, B, W, X, Y :unsigned byte;

Z :unsigned integer, (each integer is represented by two

bytes)

begin

X :=A+B

Y :=abs(bA-b);

W :=A-B

Z :=A*B

End;





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4. (a) Consider the following Pascal function where A and B are non-zero positive integers. What is the value of GET(3,2)?

function GET(A,B:integer);integer;

begin

if B = 0 then

GET:=1

else if A < B then

GET:=0

else

GET:=GET(A-1,B)+GET(A-1,B-1)

end ;

(b) The Pascal procedure given for computing the transpose of an N × N (N>1)

matrix A of integers has an error. Find the error and correct it.

Assume that the following declaration are made in the main program

const

MAXSIZE=20;

type

INTARR=array [1.,MAXSIZE,1..MAXSIZE] of integer;

Procedure TRANSPOSE (var A: INTARR; N : integer);

var

I, J, TMP, integer;

begin

for I:=1 to NO – 1 do

for J:=1 to N do

begin

TMP: = A[I,J];

A[I,J]:=A[J,I];

A(J,I:=TMP

end

end;

5. A computer installation has 1000k of main memory. The jobs arrive and finish in

the following sequences.

Job 1 requiring 200k arrives



Job 1 finishes






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(a) Draw the memory allocation table using Best Fit and First fit algorithms.

(b) Which algorithm performs better for this sequence?

6. What is the number of binary trees with 3 nodes which when traversed in post-

order give the sequence A, B, C? Draw all these binary trees.

7. (a) Determine the number of divisors of 600.

(b) Compute without using power series expansion 0

sinlim

0x

x

→

SECTION – B

Answer any TEN questions.

8. Construct the LL(1) table for the following grammar.

1. Expr _Expr

2. Expr (Expr)

3. Expr Var Expr Tail

4. ExprTail _Expr

5. ExprTail λ

6. Var Id Var Tail

7. VarTail (Expr)

8. VarTail λ

9. Goal Expr$

9. (a) Translate the arithmetic expression ( )*a b c− + into syntax tree.

(b) A grammar is said to have cycles if it is the case that

A

A ⇒ +

Show that no grammar that has cycles can be LL(I).

10. (a) Using the scope rules of Pascal determine the declaration that apply to each

occurrence of the names A and B in the following program segment.

procedure T(U, V, X, Y: integer);

var

A: record

A, B : integer

end;





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B: record

B, A : integer

end;

begin

with A do

begin

A:=4;

B:=V

end;

with B do

begin

A:=X;

B:=Y

end

end;

(b) Find the lexical errors in the following Pascal statement:

if A > 1, then B = 2.5A else read (C);

11. Let L be a language over ∑ i.e., *L ≤ ∑ . Suppose L satisfies the two conditions

given below

(i) L is in NP and

(ii) For every n, there is exactly one string of length n that belongs to L.

Let cL be the complement of L over *∑ . Show that cL is also in NP.

12. Consider the following sequence of numbers

92, 37, 52, 12, 11, 25

Use bubblesort to arrange the sequence in ascending order. Give the sequence at

the end of each of the first five passes.

13. Obtain the principal (canonical) conjunctive normal form of the propositional

formula

( ) ( )p q V q r∧ ¬ ∧

Where ‘ ∧ ’ is logical and, ‘v’ is inclusive or and ¬ is negation.

14. If the overhead for formatting a disk is 96 bytes for 4000 byte sector,

(a) Compute the unformatted capacity of the disk for the following parameters:

Number of surfaces: 8

Outer diameter of the disk: 12 cm

Inner diameter of the disk: 4 cm

Inter track space: 0.1 mm





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Number of sectors per track: 20

(b) if the disk in (a) is rotating at 360 rpm, determine the effective data transfer

rate which is defined as the number of bytes transferred per second between disk and memory.

15. (a) Implement a circuit having the following output expression using an inverter

and NAND gate .Z A B C= + +

(b) What is the equivalent minimal Boolean expression (in sum of products form) for the Karnaugh map given below?

16. The following is an 8085 assembly language program:

MVI B, OAH

MVI A, 05H

LXI H, IC40H

CALL SUB

HLT

SUB CMP M

RZ

INX H

DCR B

JNZ SUB

RET

(a) What does the program do?

(b) What are the contents of registers A and B initially?

(c) What are the contents of HL register pair after the execution of the program?

17. (a) An asynchronous serial communication controller that uses a start stop

scheme for controlling the serial I/O of a system is programmed for a string

of length seven bits, one parity bit (odd parity) and one step bit. The transmission rate is 1200 bits/second.

(i) What is the complete bit stream that is transmitted for the string ‘0110101’?

(ii) How many such strings can be transmitted per second?

1

1

1

00 01 11 10

00

01

11

10

CD

AB

1

1 1

1

1





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(b) Consider a CRT display that has a text mode display format of 80 × 25

characters with a 9 × 12 character cell. What is the size of the video buffer

RAM for the display to be used in monochrome (1 bit per pixel) graphics

mode?

18. The following is an incomplete Pascal function to convert a given decimal integer

(in the range -8 to +7) into a binary integer in 2’s complement representation. Determine the expression A, B, C that complete program.

function TWOSCOMP (N:integer):integer;

var

RAM, EXPONENT:integer;

BINARY :integer;

begin

if(N>=-8) and (N<=+7) then

begin

if N<0 then

N : = A;

BINARY:=0;

EXPONENT:=1;

while N<>0 do

begin

REM:=N mod 2;

BINARY:=BINARY + B*EXPONENT;

EXPONENT:=EXPONENT*10;

N :=C

end

TWOSCOMP:=BINARY

end

end;

19. Consider the following program segment for concurrent processing using

semaphore operators P and V for synchronization. Draw the precedence graph for the statements S1 to S9.

var

a, b, c, d, e, f, g, h, i, j, k : semaphore;

begin

cobegin

begin S1; V(a); V(b) end;

begin P(a); S2; V(c); V(d) end;

begin P(c); S4; V(c) end;





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begin P(d); S5; V(f) end;

begin P(e); P(f); S7; V(k) end;

begin P(b); S3;V(g);V(h) end;

begin P(g); S6; V(i) end;

begin P(h); P(i); S8; V(j) end;

begin P(j); P(j); P(k); S9 end;

coend

end;

20. The head of a moving head disk with 100 tracks numbered 0 to 99 is currently

serving a request at tract 55. If the queue of requests kept in FIFO order is

10, 70, 75, 23, 65

Which of the two disk scheduling algorithms FCFS (First Come First Served) and

SSTF (Shortest Seek Time First) will require less head movement? Find the head

movement for each of the algorithms.

21. Let 1 2 and G G be subgroups of a group G.

(a) Show that 1 2G G∩ is also a group of G

(b) Is 1 2G G∪ always a subgroup of G?

22. How many minimum spanning trees does the following graph have? Draw them.

(Weights are assigned to the edge).

23. Prove using mathematical induction for 25,2nn n≥ >

24. Prove that in finite graph, the number of vertices of odd degree is always even.

25. (a) Find the minimum value of 23 4 2 .x x− +

(b) Determine the number of positive integers ( )720≤ which are not divisibly by

any of numbers 2, 3, and 5.

A B

C

D E

2

3

5

4

3

4





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26. (a) Consider the relation scheme R(A, B, C) with the following functional dependencies:

A, B C, C A

Show that the scheme R is the Third Normal Form (3NF) but not in Boyce-

Code Normal Form (BCNF).

(b) Determine the minimal keys of relation R.

27. Consider the relation scheme.

AUTHOR (ANAME, INSTITUTION, ACITY, AGE)

PUBLISHER (PNAME, PCITY)

BOOK (TITLE, ANAME, PNAME)

Express the following queries using (one or more of )SELECT, PROJECT, JOIN and

DIVIDE operations.

(a) Get the names of all publishers.

(b) Get values of all attributes of all authors who have published a book for the

publisher with PNAME = ‘TECHNICAL PUBLISHERS’.

(c) Get the names of all authors who have published a book for any publisher

located in Madras.





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SECTION - A

1. Write in your answer book the correct or the most appropriate answer to the

following multiple choice questions by writing the corresponding letter a, b, c or d against the sub-question number.

1.1 Let A and B be sets and let and c cA B denote the complements of the sets A and

B. the set (a – b) ∪(b-a) ∪(a∩b) is equal to.

(a) A ∪ B (b) c cA B∪ (c) A ∩ B (d) c cA B∩

1.2 Let X = 2,3,6,12,24, Let ≤ be the partial order defined by X ≤ Y if x divides y.

Number of edge as in the Hasse diagram of (X,≤) is

(a) 3 (b) 4

(c) 9 (d) None of the above

1.3 Suppose X and Y are sets and and X Y are their respective cardinalities. It is

given that there are exactly 97 functions from X to Y. from this one can conclude that

(a) 1, 97X Y= = (b) 97, 1X Y= =

(c) 97, 97X Y= = (d) None of the above

1.4 Which of the following statements is false?

(a) The set of rational numbers is an abelian group under addition.

(b) The set of integers in an abelian group under addition.

(c) The set of rational numbers form an abelian group under multiplication.

(d) The set of real numbers excluding zero in an abelian group under

multiplication.

1.5 Two dice are thrown simultaneously. The probability that at least one of them will

have 6 facing up is

(a) 1

36 (b)

1

3 (c)

25

36 (d)

11

36

1.6 The formula used to compute an approximation for the second derivative of a

function f at a point X0 is.

(a) ( ) ( )0 0

2

f x h f x h+ + − (b)

( ) ( )0 0

2

f x h f x h

h

+ − −

(c) ( ) ( ) ( )0 0 0

2

2f x h f x f x h

h

+ + + − (d)

( ) ( ) ( )0 0 0

2

2f x h f x f x h

h

+ − + −





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1.7 Let Ax = b be a system of linear equations where A is an m × n matrix and b is a

m × 1 column vector and X is a n × 1 column vector of unknows. Which of the

following is false?

(a) The system has a solution if and only if, both A and the augmented matrix [A

b] have the same rank.

(b) If m < n and b is the zero vector, then the system has infinitely many

solutions.

(c) If m = n and b is non-zero vector, then the system has a unique solution.

(d) The system will have only a trivial solution when m = n, b is the zero vector and rank (A) = n.

1.8 Which two of the following four regular expressions are equivalent? (ε is the

empty string).

(i) (00) * (ε + 0)

(ii) (00)*

(iii) 0*

(iv) 0(00)*

(a) (i) and (ii) (b) (ii) and (iii) (c) (i) and (iii) (d) (iii) and (iv)


(a) The Halting problem of Turing machines is undecidable.

(b) Determining whether a context-free grammar is ambiguous is undecidbale.

(c) Given two arbitrary context-free grammars G1 and G2 it is undecidable

whether L(G1) = L(G2).

(d) Given two regular grammars G1 and G2 it is undecidable whether L(G1) =

L(G2).

1.10 Let L ⊆ Σ* where Σ = a, b. which of the following is true?

(a) has an equal number of a's and b's is regularL x x=

(b) 1 is regularn nL a b n= ≥

(c) has more a's and b's is regularL x x=

(d) , 1 is regularm nL a b m n= ≥ ≥

1.11 Which of the following is false?

(a) log

100 log100

n nn

=

(b) ( )log 0 loglogn n=

(c) ( )If 0 then 0x yx y n n< < = (d) ( )2 0n nk≠





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1.12 Consider the following statements:

(i) First-in-first out types of computations are efficiently supported by STACKS.

(ii) Implementing LISTS on linked lists is more efficient than implementing LISTS on an array for almost all the basic LIST operations.

(iii) Implementing QUEUES on a circular array is more efficient than

implementing QUEUES on a linear array with two indices.

(iv) Last-in-first-out type of computations are efficiently supported by QUEUES.

(a) (ii) and (iii) are true (b) (i) and (ii) are true

(c) (iii) and (iv) are true (d) (ii) and (iv) are true

1.13 An advantage of chained hash table (external hashing) over the open addressing

scheme is

(a) Worst case complexity of search operations is less?

(b) Space used is less (c) Deletion is easier


1.14 In the balanced binary tree in Fig.1.14 given below, how many nodes will become

unbalanced when a node is inserted as a child of the node “g”?

(a) 1 (b) 3 (c) 7 (d) 8

1.15 Which of the following sequences denotes the post order traversal sequence of

the tree of question 1.14?

(a) f e g c d b a (b) g c b d a f e (c) g c d b f e a (d) f e d g c b a

1.16 Relative mode of addressing is most relevant to writing

(a) coroutines (b) position – independent code

(c) shareable code (d) interrupt handlers

1.17 The pass numbers for each of the following activities

(i) object code generation

(ii) literals added to literal table

(iii) listing printed

(iv) address resolution of local symbols that occur in a two pass assembler respectively are

(a) 1, 2, 1, 2 (b) 2, 1, 2, 1 (c) 2, 1, 1, 2 (d) 1, 2, 2, 2

a

b

c

g

d f

e





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1.18 The process state transition diagram in Fig.1.8 is representative of

(a) a batch operating system

(b) an operating system with a preemptive scheduler

(c) an operating system with a non-preemptive scheduler

(d) a uni-programmed operating system.

1.19. A critical section is a program segment

(a) which should run in a certain specified amount of time

(b) which avoids deadlocks

(c) where shared resources are accessed

(d) which must be enclosed by a pair of semaphore operations, P and V

1.20. Which of the following is an example of spooled device?

(a) A line printer used to print the output of a number of jobs.

(b) A terminal used to enter input data to a running program.

(c) A secondary storage device in a virtual memory sytem.

(d) A graphic display device.

1.21. A ROM is sued to store the table for multiplication of two 8-bit unsigned integers. The size of ROM required is

(a) 256 × 16 (b) 64 K × 8 (c) 4 K × 16 (d) 64 K × 16

1.22. Number of machine cycles required for RET instruction in 8085 microprocessor is

(a) 1 (b) 2 (c) 3 (d) 5

1.23. Both’s algorithm for integer multiplication gives worst performance when the

multiplier pattern is

(a) 101010 …..1010 (b) 100000 …..0001

(c) 111111 …..1111 (d) 011111 …..1110

TERMINATED

RUNNING

BLOCKED

READY

NEW





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1.24. For the daisy chain scheme of connecting I/O devices, which of the following

statements is true?

(a) It gives non-uniform priority to various devices.

(b) It gives uniform priority to all devices.

(c) It is only useful for connecting slow devices to a processor device.

(d) It requires a separate interrupt pin on the processor for each device.

1.25 Consider the following floating-point number representation.

31 24 23 0

Exponent Mantissa

The exponent is in 2’s complement representation and mantissa is in the sign

magnitude representation. The range of the magnitude of the normalized numbers in this representation is

(a) 0 to 1 (b) 0.5 to 1

(c) 232 to 0.5− (d) ( )-230.5 to 1-2

2. Write in your answer book the correct or the most appropriate answer to the

following multiple choice questions by writing the corresponding letter a, b, c or d

against the sub-question number.

2.1 Let R denotes the set of real numbers. Let f:R×R R×R be a bijective function

defined by f(x,y)=(x+y,x-y). the inverse function of f is given by

(a) ( )1 1 1, ,f x y

x y x y

− =

+ − (b) ( ) ( )1 , ,f x y x y x y− = − +

(c) ( )1 , ,2 2

x y x yf x y− + −

=

(d) ( ) ( ) ( )1 , 2 ,2f x y x y x y− = − +

2.2. Let R be a non-empty relation on a collection of sets defined by A R B if and only

if A ∩ B = φ. Then, (pick the true statement)

(a) R is reflexive and transitive

(b) R is symmetric and not transitive

(c) R is an equivalence relation

(d) R is not reflexive and not symmetric





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2.3. Which of the following is false? Read ∧ as AND, ∨ as OR, ~ as NOT, as one way

implication and ↔ as two way implication.

(a) ( )( )x y x y→ ∧ → (b) ( ) ( )( )x y x y x→ ∧ ∧ →

(c) ( )( )x x ψ→ ∨ (d) ( ) ( )( )x y x y∨ ↔ →

2.4. Which one of the following is false?

(a) The set of all bijective functions on a finite set forms a group under function

composition.

(b) The set 1,2, ……., p –1 forms a group under multiplication mod p where p

is a prime number.

(c) The set of all strings over a finite alphabet forms a group under

concatenation.

(d) A subset s ≠ φ of G is a subgroup of the group <G, *> if and only if for any

pair of elements a, b ∈ s, a* b-1 ∈ s.

2.5. Newton-Raphson iteration formula for finding 3 ,c where c > 0 is,

(a) 3

1 2

2 3

3

nn

n

x cx

x+

+= (b)

3

1 2

2 3

3

nn

n

x cx

x+

−=

(c) 3

1 2

2

3

nn

n

x cx

x+

+= (d)

3

1 2

2

3

nn

n

x cx

x+

−=

2.6. The matrices cos sin 0

and sin cos 0

a

b

θ θ

θ θ

−

commute under multiplication

(a) if a = b or θ = nπ, is an integer (b) always

(c) never (d) if a cos θ ≠ b sin θ

2.7. The probability that top and bottom cards of a randomly shuffled deck are both

aces in

(a) 4 4

52 52× (b)

4 3

52 52× (c)

4 3

52 51× (d)

4 4

52 51×

2.8. If L1 and L2 are context free languages and R a regular set, one of the languages

below is not necessarily a context free language. Which one?

(a) L1, L2 (b) L1 ∩ L2 (c) L1 ∩ R (d) L1 ∪ L2





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2.9. Define a context free languages L ≤ 0,1 init (L) = u/uv ∈ L for some ν in

0,1 (in other words, init(L) is the set of prefixes of L)

Let L w/w is nonempty and has on equal number of 0’s and 1’s

Then init (L) is

(a) the set of all binary strings with unequal number of 0’s and 1’s

(b) the set of all binary strings including the null string

(c) the set of all binary strings with exactly one more 0’s than the number of 1’s

or one more 1 than the number of 0’s.


2.10. The grammar whose productions are

if id then <stmt>

if id then <stmt> else <stmt>

id:=id

is ambiguous because

(a) the sentence

if a then if b then c:=d

(b) the left most and right most derivations of the sentence

if a then if b then c:=d

give rise top different parse trees

(c) the sentence

if a then if b then c:=d else c:=f

has more than two parse trees

(d) the sentence

if a then if then c:=d else c:=f

has two parse trees

2.11. The minimum number of interchanges needed to convert the array

89, 19, 40, 17, 12, 10, 2, 5, 7, 11, 6, 9, 70

(a) 0 (b) 1 (c) 2 (d) 3

2.12. The recurrence relation

T(1) = 2

T(n) = 34

nT n

+

Has the solution T(n) equal to

(a) O(n) (b) O (log n)

(c) O

3

4n






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2.13. The average number of key comparisons done on a successful sequential search

in list of length n is

(a) log n (b) 1

2

n − (c)

2

n (d)

1

2

n +

2.14. A binary search tree is generated by inserting in order the following integers:

50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24

The number of nodes in the left subtree and right subtree of the root respectively

is

(a) (4, 7) (b) (7, 4) (c) (8, 3) (d) (3, 8)

2.15. Quick-sort is run on two inputs shown below to sort in ascending order

(i) 1,2,3 ….n

(ii) n, n – 1, n – 2, …. 2, 1

Let C1 and C2 be the number of comparisons made for the inputs (i) and (ii)

respectively. Then,

(a) C1 < C2 (b) C1 > C2 (c) C1 = C2

(d) we cannot say anything for arbitrary n.

2.16. Which of the following macros can put a macro assembler into an infinite loop?

(i) MACRO M1, X

IF EQ, X: if X=0 then ….

M1 X + 1

ENDC

IF NE, X: if X ≠ O then ……

WORD X: address (X) is stored here

ENDC

ENDM

(ii) MACRO M2,X

IF EQ, X

M2 X

ENDC

IF NE, X

WORD X + 1

ENDC

ENDM

(a) (ii) only (b) (i) only

(c) both (i) and (ii) (d) None of the above





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2.17. The correct matching for the following pairs is

(A) Activation record (1) Linking loader

(B) Location counter (2) Garbage collection

(C) Reference counts (3) Subroutine call

(D) Address relocation (4) Assembler

(a) A – 3 B – 4 C – 1 D - 2 (b) A – 4 B – 3 C – 1 D - 2

(c) A – 4 B – 3 C – 2 D - 1 (d) A – 3 B – 4 C – 2 D - 1

2.18. A 1000 Kbyte memory is managed using variable partitions but to compaction. It

currently has two partitions of sizes 200 Kbytes and 260 Kbytes respectively. The smallest allocation request in Kbytes that could be denied is for

(a) 151 (b) 181 (c) 231 (d) 541

2.19. A solution to the Dining Philosophers Problem which avoids deadlock is

(a) ensure that all philosophers pick up the left fork before the right fork

(b) ensure that all philosophers pick up the right fork before the left fork

(c) ensure that one particular philosopher picks up the left fork before the right

fork, and that all other philosophers pick up the right fork before the left fork


2.20. Four jobs to be executed on a single processor system arrive at time 0+ in the

order A, B, C, D. their burst CPU time requirements are 4, 1, 8, 1 time units

respectively. The completion time of A under round robin scheduling with time

slice of one time unit is

(a) 10 (b) 4 (c) 8 (d) 9

2.21. Consider the circuit in Fig.2.21 which has a four fit binary number 3 2 1 0b b b b as

input and a five bit binary number, 4 3 2 1 0d d d d d as output.

(a) Binary of Hex conversion

(b) Binary to BCD conversion

(c) Binary to grey code conversion

(d) Binary to radix-12 conversion.

‘φ’

b3 b2 b1 b0

d2 d1 d0 d3

d4

‘φ’ C out

Binary adder

C in





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2.22. Consider the circuit in Fig.2.22 f implements

(a) A BC ABC ABC+ + (b) A + B + C

(c) A B C⊕ ⊕ (d) AB+BC+CA

2.23. Consider the following state table in Fig.2.23 for a sequential machine. The

number of states in the minimized machine will be

(a) 4 (b) 3 (c) 2 (d) 1

2.24. What is the equivalent Boolean expression in product-of-sums form for the

Karnaugh map given in Fig.2.24.

(a) BD BD+

(b) ( ) ( )B C D B C D+ + + +

(c) ( ) ( )B D B D+ +

(d) ( ) ( )B D B D+ +

2.25. A micro program control unit is required to generate a total of 25 control signals.

Assume that during any microinstruction, at most two control signals are active.

Minimum number of bits required in the control word to generate the required control signals will be

(a) 2 (b) 2.5 (c) 10 (d) 12

1

1

1

1

1

00 01 11 20

00

01

11

10

CD

AB

1

1

1

B1

input

C1 A0

D0

0 1

A

D

B

C

Present state

x

B1

A1

A0

C1

A B

C

C

C

f Multiplex C

0

1

2

3





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3. Let f be a function defined by

( )

2

2

for 1

for 1 2

for 2

x x

f x ax bx c x

x d x

≤

= + + ≤

+ >

Find the values for the constants a; b; c and d so that f is continuous and differentiable everywhere on the real line.

4. A binary search tree is used to locate the number 43. Which of the following

probe sequences are possible and which are not? Explain.

(a) 61 52 14 17 40 43

(b) 2 3 50 40 60 43

(c) 10 65 31 48 37 43

(d) 81 61 52 14 41 43

(e) 17 77 27 66 18 43

5. A logic network has two data inputs A and B, and two control inputs C0 and C1. It

implements the function F according to the following table.

C1 C2 F

0 0 A B+

0 1 A + B

1 0 A B⊕

Implement the circuit using one 4 to AB Multiplexor, one 2-input Exclusive OR

gate, one 2-input AND gate, one 2-input OR gate and one Inverter.

6. An 8085 based system has an output port with address 00H. Consider the

following assembly language program.

ORG 0100H

MVI A, 00H

LXI H, 0105H

PCHL

HLT

(a) What does the program do with respect to the output port φφ H?

(b) Show the waveforms at the three least significant bits of the port φφ H.





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7. A demand paged virtual memory system uses 16 bit virtual address, page size of

256 bytes, and has 1 Kbyte of main memory. LRU page replacement is

implemented using list, whose current status (page numbers in decimal) is

LRU page

For each hexadecimal address in the address sequence given below,

00FF, 010D, 10FF 11B0

indicate,

(i) the new status of the list

(ii) page faults, if any, and

(iii) page replacements, if any.

SECTION – B

Answer any TEN questions from this section. All questions carry equal marks.

8. Let F be the collection of all functions f:1,2,3 1,2,3. If f and g ∈ F, define

an equivalence relation ~ by f ~ g if and only if f(3) = g.

(a) Find the number of equivalence classes defined by ~

(b) Find the number of elements in each equivalence class.

9. The Fibonacci sequence 1 2 3, , nf f f fK is defined by the following recurrence:

2 1 2 1, 1; 1: 1:n n nf f f n f f+ += + ≥ = =

Prove by induction that every third element of the sequence is even.

10. Let 11 12 11 12

21 22 21 22

and a a b b

A Ba a b b

= =

be two matrices such that

AB = I. Let 1 0

1 1C A

=

and CD = 1. Express the elements of D in terms of the

elements of B.

11. Let G be a context-free grammar where G = (S, A, B, C, a, b, d, P,S) with

the productions in P given below.

S ABAC

A aA|ε

B bB ε

C d

17 1 63





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(ε denoted the null string). Transform the grammar G to an equivalent context-

free grammar G that has no ε productions and no unit productions. ( A unit

production is of the form x y, and y are non terminals).

12. Given below are the transition diagrams (Fig.12) for two finite state machines M1

and M2 recognizing languages L1 and L2 respectively.

(a) Display the transition diagram for a machine that recognizes L1 L2, obtained

from transition diagrams for M1 and M2 by adding only and transitions and no new states.

(b) Modify the transition diagram obtained in part (a) obtain a transition diagram

for a machine that recognizes (L1 L2) by adding only ε transitions and no new

states.

(Final states are enclosed in double circles).

13. Let Q = (q1, q2) (a,b), (a, b, Z) δ, qi, Z, φ) be a pushdown automaton accepting

by empty stack for the language which is the set of all nonempty even

palindromes over the set a,b. Below is an incomplete specification of the

transition d. complete the specification. The top of stack is assumed to be at the right end of the string representing stack contents.

(1) ( ) ( ) 1 1, , ,q a Z q Zaδ =

(2) ( ) ( ) 1 1, , ,q b Z q Zbδ =

(3) ( ) 1, , ,q a aδ = KK KK

(4) ( ) 1, , ,q b bδ = KK KK

(5) ( ) ( ) 2 2, , ,q a a qδ ε=

(6) ( ) ( ) 2 2, , ,q b b qδ ε=

(7) ( ) ( ) 2 2, , ,q Z qδ ε ε=

A B

0

1

0

1

Start M1

C E D Start

a

b

b

a

a

b





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14. A two dimensional array A[1- n] [1 – n] of integers is partially sorted if

, 1 1 1 and

1

i j n A i j A i j

A i j A i j

ε∀ − − < +

< +

Fill in the blanks:

(a) The smallest item in the array is at A[i] [j] where i =

and j = …………

(b) The smallest item is deleted. Complete the following O(n) procedure to insert

item x (which is guaranteed to be smaller than any item in the last row or

column) still keeping A partially sorted.

procedure insert (x integer)

var j ′ j:integer;

begin

(1) i: =1; j:=A[i] [j]:=x;

(2) while (x > or x >) do

(3) if A[ i + 1] [j] ∩ [i] ]j] then begin

(4) A [i] [j]:= A[i +1] [j]; i: =i + 1

(5) end

(6) else begin

(7)

(8) end

(9) A [i] [j]:=

end

15. Insert the characters of the string K R P C S N Y T J M into a hash table of size

10.

Use the hash funtion

H(x) = (ord (x) – ord (‘a’) + 1) mod 10

And linear probing to resolve collisions.

(a) Which insertions cause collisions?

(b) Display the final hash table?

16. A complete, undirected, weighted graph G is given on the vertex 0, 1 …., n – 1

for any fixed ‘n’. Draw the minimum spanning tree of G if

(a) the weight of the edge (u, v) is |u – v|

(b) the weight of the edge (u, v) is u + v





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17. Let G be the directed, weighted graph shown below in Fig.4

We are interested in the shortest paths from A.

(a) Output the sequence of vertices identified by the Dijkstra’s algorithm for

single source shortest path when the algorithm is started at node A.

(b) Write down sequence of vertices in the shortest path from A to E.

(c) What is the cost of the shortest path from A to E?

18. Consider the following program that attempts to locate an element x in an array

a [ ] using binary search. Assume N > 1. The program is erroneous. Under what

conditions does the program fail?

var i.j.k:integer; x:integer.

a:=array; [1 … N] of integer.

begin i:1;=n;

repeat k:(i+j) div 2;

if a [k] < x then i:=k

else j:=k

until (a =x) or (i∩=j);

if (a [k] = x) then

writeln (‘x is not in the array’)

else

writeln (‘x’ is not in the array’)

end;

19. Consider the following program in pseudo-Pascal syntax. What is printed by the

program if parameter a is procedure test 1 is passed as

(i) call-by-reference parameter?

(ii) call-by-value-result parameter?

program Example (input, output)

var b: integer;

procedure test 2;

A

B

C

D E

F

41

22 12 6

2 12

15 7φ

5φ

1φ

6φ

9φ





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begin b: = 10 end

procedure test 1 (a:integer);

begin a:5;

writeln (‘point 1: ‘a,b);

test 2;

wrote;m(‘point: ‘a,b);

end;

begin (*Example*)

b:=3; test ] (b);

writeln (‘point 3: ‘b)

end

20. Consider the syntax-directed translation schema (SETS) shown below:

E E + E print “+”

E E * E print “.”

E id print id.name

E (E)

An LR – parser executes the actions associated with the productions immediately

after a reduction by the corresponding production. Draw the parse tree and write the translation for the sentence.

(a + b)* (c + d), using SDTS given above.

21. The concurrent programming constructs fork and join are as below:

fork <label> which creates a new process executing from the specified label

join <variable> which decrements the specified synchronization variable (by 1)

and terminates the process if the new value is not 0.

Show the precedence graph for S1, S2, S3, S4 and S5 of the concurrent program below.

N = 2

M = 2

fork L3

fork L4

S1

L1 : join N

S3

L2: join M

S5

L3:S2

goto L1

L4:S4





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goto L2

next:

22. A computer system uses the Banker’s Algorithm to deal with deadlocks. Its

current state is shown in the tables below, where P0, P1, P2 are processes, and R0, R1, R2 are resoures types.

Maximum Need Current Allocation Available

R0 R1 R2 R0 R1 R2 R0 R1 R2

P0 4 1 2 P0 1 0 2 2 2 0

P1 1 5 1 P1 0 3 1

P2 1 2 3 P2 1 0 2

(a) Show that the system can be in this state.

(b) What will system do on a request by process P0 for one unit of resource type

R1?

23. A file system with a one-level directory structure is implemented on a disk with

disk block size of 4 K bytes. The disk is used as follows:

Disk-block 0: File Allocation Table, consisting of one 8-bit entry per date

block, representing the data block address of the next date block in the file

Disk block 1: Directory, with one 32 bit entry per file:

Disk block 2: Data block 1;

Disk block 3: Data block 2; etc.

(a) What is the maximum possible number of files?

(b) What is the maximum possible file size in blocks?

24. Consider the synchronous sequential circuit in Fig.5.

(a) Draw a state diagram, which is implemented by the circuit. Use the following

names for the states corresponding to the values of flip-flops as given below.

D1 Q1

CK

D2 Q2

CK

D3 Q3

CK

Clock

Fig.5





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Q1 Q2 Q3 State

0 0 0 S0

0 0 1 S1

- - - -

- - - -

- - - -

1 1 1 S7

(b) Given that the initial of the circuit is S4, identify the set of states, which are not reachable.

25. A hard disk is connected to a 50 MHz processor through a DMA controller.

Assume that the initial set-up of a DMA transfer takes 1000 lock cycles for the

processor, and assume that the handling of the interrupt at DMA completion

requires 500 clock cycles for the processor. The hard disk has a transfer rate of

2000 Kbytes/sec and average block size transferred is 4 K bytes. What fraction of

the processor time is consumed by the disk, if the disk is actively transferring 100% of the time?

Level 1 (Cache memory) Level 1 (Cache memory)

Access time = 50 nsec/byte Access time = 200 nsec/byte

Size Hit ratio Size Hit ratio

8 Kbytes 0.80 4 Kbytes 0.98



Size Hit ratio

250 M bytes 1.0

26. A computer system has a three level memory hierarchy, with access time and hit

ratios as shown below:

Level 1 (Cache memory) Level 2 (main memory) Level 3

Access time = 50 nsec/byte Access time = 200 nsec/byte Access time = 5 µsec/byte

Size Hit ratio

Size Hit ratio

Size Hit ratio

8 M byte 0.80 4M byte 0.98 260 Mbyte 1.0

16 M byte 0.90 16 M byte 0.99





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64 M byte 0.95 64 M byte 0.995

(a) What should be the minimum sizes of level 1 and 2 memories to achieve an average access time of less than 100 nsec?

(b) What is the average access time achieved using the chosen sizes of level 1

and level 2 memories?

27. A library relational database system uses the following schema

USERS (User #, User Name, Home Town)

BOOKS (Books # Book Title, Author Name)

ISSUED (Book #, User #, Date)

Explain in one English sentence, what each of the following relational algebra

queries is designed to determine

(a) σ User #=6 (11 User #, Book Title ((USERS ISSUED) BOOKS))

(b) σ Author Name (BOOKS (σ Home Town) = Delhi (USERS ISSUED)))





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SECTION – A

1. This question contains 10 sub-parts each carrying ONE mark. Each sub-part

contains a multiple-choice question. Write in your answer book the sub-part number and the letter a, b, c or d corresponding to the most appropriate answer.

1.1 The probability that it will rain today is 0.5. The probability that it will rain

tomorrow is 0.6. The probability that it will rain either today or tomorrow is 0.7. What is the probability that it will rain today and tomorrow?

(a) 0.3 (b) 0.25 (c) 0.35 (d) 0.4

1.2 The Newton-Raphson method is used to find the root of the equation 2 2 0x − = .

If the iterations are started form –1, the iterations will

(a) converge to -1 (b) converge to 2

(c) converge to - 2 (d) not converge

1.3 The determinant of the matrix

6 8 1 1

0 2 4 6

0 0 4 8

0 0 0 1

−

−

is:

(a) 11 (b) -48 (c) 0 (d) -24

1.4 The concatenation of two lists is to be performed on 0(1) time. Which of the

following implementations of a list should be used?

(a) Singly linked list (b) Doubly linked list

(c) Circular doubly linked list (d) Array implementation of list

1.5 The correct matching for the following pairs is

(A) All pairs shortest paths (1) Greedy

(B) Quick Sort (2) Depth-First search

(C) Minimum weight spanning tree (3) Dynamic Programming

(D) Connected Components (4) Divide and Conquer

(a) A – 2 B – 4 C – 1 D - 3 (b) A – 3 B – 4 C – 1 D - 2

(c) A – 3 B – 4 C – 2 D - 1 (d) A – 4 B – 1 C – 2 D - 3





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1.6 In the following grammar

::

:: *

::

YX X

Y

YY Z

Z

Z id

= ⊕

=

=


(a) ‘⊕’ is left associative while ‘*’ is right associative

(b) Both ‘⊕’ and ‘*’ is left associative

(c) ‘⊕’ is right associative while ‘*’ is left associative


1.7 Which of the following is essential for converting an infix expression to the postfix

form efficiently?

(a) An operator stack (b) An operand stack

(c) An operand stack and an operator stack

(d) A parse tree

1.8 A language L allows declaration of arrays whose sizes are not known during

compilation. It is required to make efficient use of memory. Which one of the following is true?

(a) A compiler using static memory allocation can be written for L

(b) A compiler cannot be written for L; an interpreter must be used.

(c) A compiler using dynamic memory allocation can be written for L


1.9 The conditional expansion facility of macro processor is provided to

(a) test a condition during the execution of the expanded program

(b) to expand certain model statements depending upon the value of a condition

during the execution of the expanded program

(c) to implement recursion

(d) to expand certain model statements depending upon the value of a condition

during the process of macro expansion.

1.10 Heap allocation is required for languages.

(a) that support recursion

(b) that support dynamic data structures

(c) that use dynamic scope rules






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2. The question contains 5 subparts, each carrying 1 mark. Each subpart contains a

multiple-choice question. Write in your answer book the subpart number and the

letter a, b, c or d corresponding to the most appropriate answer.

2.1 Let * be defined as x*y= x +y. Let z = x*y. value of z*x is

(a) x +y (b) x (c) 0 (d) 1

2.2 RST 7.5 interrupt in 8085 microprocessor executes service routing from interrupt

vector location

(a) 0000H (b) 0075H (c) 003CH (d) 0034H

2.3 Purpose of a start bit in RS 232 serial communication protocol is

(a) to synchronize receiver for receiving every byte

(b) to synchronize receiver for receiving a sequence of bytes

(c) a parity bit

(d) to synchronize receiver for receiving the last byte

2.4 The correct matching for the following pairs is

(A) DMA I/O (1) High speed RAM

(B) Cache (2) Disk

(C) Interrupt I/O (3) Printer

(D) Condition Code Register (4) ALU

(a) A – 4 B – 3 C – 1 D - 2 (b) A – 2 B – 1 C – 3 D - 4

(c) A – 4 B – 3 C – 2 D - 1 (d) A – 2 B – 3 C – 4 D - 1

2.5 An N-bit carry lookhead adder, where N is a multiple of 4, employs ICs 74181 (4

bit ALU) and 74182 (4 bit carry lookhead generator).

The minimum addition time using the best architecture for this adder is

(a) proportional to N (b) proportional to log N

(c) a constant (d) None of the above

3. The question contains 10 subparts, each carrying 1 mark. Each subpart contains

a multiple-choice question. Write in your answer book the subpart number and the letter a, b, c or d corresponding to the most appropriate answer.

3.1 Let (Z,*) be an algebraic structure, where Z is the set of integers and the

operation * is defined by n*m = maximum (n,m). which of the following statements is true for (Z,*)?

(a) (Z,*) is a monoid (b) (Z,*) is an Abelian group

(c) (Z,*) is a group (d) None of the above





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3.2 Which of the following propositions is a tautology?

(a) (p ∨ q) p (b) p ∨ (q p) (c) p ∨ (p q) (d) p (p q)

3.3 In the lattice defined by the Hasse diagram given in following figure, how many

complements does the element ‘e’ have?

(a) 2

(b) 3

(c) 0

(d) 1

3.4 Given Σ=a,b, which one of the following sets is not countable?

(a) Set of all strings over Σ

(b) Set of all languages over Σ

(c) Set of all regular languages over Σ

(d) Set of all languages over Σ accepted by Turing machines

3.5 Locality of reference implies that the page reference being made by a process

(a) will always be to the page used in the previous page reference

(b) is likely to be to one of the pages used in the last few page references

(c) will always be to one of the pages existing in memory

(d) will always lead to a page fault

3.6 The correct matching for the following pairs is:

(A) Disk scheduling (1) Round robin

(B) Batch processing (2) SCAN

(C) Time sharing (3) LIFO

(D) Interrupt processing (4) FIFO

(a) A – 3 B – 4 C – 2 D - 1 (b) A – 4 B – 3 C – 2 D - 1

(c) A – 2 B – 4 C – 1 D - 3 (d) A – 3 B – 4 C – 3 D - 2

3.7 I/O redirection

(a) implies changing the name of a file

(b) can be employed to use an existing file as input file for a program

(c) implies connection 2 programs through a pipe


a

b

e

f

d

c

g





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3.8 When an interrupt occurs, an operating system

(a) ignores the interrupt

(b) always changes state of interrupted process after processing the interrupt

(c) always resumes execution of interrupted process after processing the

interrupt

(d) may change state of interrupted process to ‘blocked’ and schedule another

process

3.9 Thrashing

(a) reduces page I/O

(b) decreases the degree of multiprogramming

(c) implies excessive page I/O

(d) improve the system performance

3.10 Dirty bit for a page in a page table

(a) helps avoid unnecessary writes on a paging device

(b) helps maintain LRU information

(c) allows only read on a page


4. The question contains 10 subparts, each carrying 2 marks. Each subpart contains


4.1 What is the maximum value of the function ( ) 22 2 6f x x x= − + in the interval

[0,2]?

(a) 6 (b) 10 (c) 12 (d) 5.5

4.2 Let a= ( )ija be an n-rowed square matrix and 12I be the matrix obtained by

interchanging the first and second rows of the n-rowed Identify matrix. Then

12AI is such that its first

(a) row is the same as its second row

(b) row is the same as the second row of A

(c) column is the same as the second column of A

(d) row is all zero

4.3 Using a forward Euler method to solve y ′′ (t) =f(t), y(0), y ′′ (0)=0 with a step size

of h, we obtain the following values of y in the first four iterations:

(a) 0, hf (0), h(f(0) + f(h)) and h(f(0) + f(h) = f(2h))

(b) 0, 0 h2 f(0) and 2h2f(0)+f(h)





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(c) 0, 0, h2f(0) 3h2f(0)

(d) 0, 0, hf(0) + h2f(0) and hf (0) + h2f(0)+hf(h)

4.4 A polynomial p(x) is such that p(0) = 5, p(1) = 4, p(2) = 9 and p(3) = 20. the

minimum degree it can have is

(a) 1 (b) 2 (c) 3 (d) 4

4.5 A binary search tree contains the value 1, 2, 3, 4, 5, 6, 7, 8. The tree is traversed

in pre-order and the values are printed out. Which of the following sequences is a valid output?

(a) 5 3 1 2 4 7 8 6 (b) 5 3 1 2 6 4 8 7

(c) 5 3 2 4 1 6 7 8 (d) 5 3 1 2 4 7 6 8

4.6 Let T(n) be the function defined by T(1) = 1, T(n) = 22

nT

+ n for n≥2.

Which of the following statements is true?

(a) ( )T n O n= (b) T(n) = O(n)

(c) T(n) = O (log n) (d) None of the above

4.7 A priority queue Q is used to implement a stack that stores characters. PUSH (C)

is implemented INSERT (Q, C, K) where K is an appropriate integer key chosen

by the implementation. POP is implemented as DELETEMIN(Q). For a sequence of

operations, the keys chosen are in

(a) non-increasing order (b) non-decreasing order

(c) strictly increasing order (d) strictly decreasing order

4.8 Given the following Pascal like program segment

Procedure A;

x,y:intger;

Procedure B;

x,z:real

S1

end B;

Procedure C;

i:integer;

S2

end C;

end A;





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The variables accessible in S1 and S2 are

(a) x or A, y, x of B and z in S1 and

x of B, y and i in S2

(b) x or B, y and z in S1 and

x of B, i and z in S2

(c) x or B, z and y in S1 and

x of A, i and y in S2


4.9 The expression (a * b) * c op….

where ‘op’ is one of ‘+’, ‘*’ and ‘↑’ (exponentiation) can be evaluated on a CPU

with a single register without storing the value of (a * b) if

(a) ‘op’ is ’+’ or ‘*’ (b) ‘op’ is ’↑’ or ‘*’ (c) ‘op’ is ’↑’ or ‘+’

(d) not possible to evaluate without storing

4.10 The trapezoidal method to numerically obtain ( )b

af x dx∫ has an error E bounded

by

( )2 max ,12

b ah f x x a b

−′′ ∈

where h is the width of the trapezoids. The minimum number of trapezoids

guaranteed to ensure E ≤ 10-4 is computing in 7 using 1

fx

= is

(a) 60 (b) 100 (c) 600 (d) 10000



5.1 Let ( ), ,f x y z x yx xz= + + be a switching function. Which one of the following is

valid?

(a) y x is a prime implicant of f (b) xz is a minterm of f

(c) xz is an implicant of f (d) y is a prime implicant of f

5.2 Contents of A register after the execution of the following 8085 microprocessor

program is

MVIA, 55 H

MVI C, 25 H

ADDC

DAA

(a) 7AH (b) 80H (c) 50H (d) 22H





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5.3 A micro instruction is to be designed to specify

(a) none or one of the three micro operations of one kind and

(b) none or upto six micro operations of another kind

The minimum number of bits in the micro-instruction is

(a) 9 (b) 5


5.4 Given ) )224 13 .r r

=

The value of the radix r is:

(a) 10 (b) 8 (c) 5 (d) 6

5.5 Consider the logic circuit shown in Figure below. The functions 1 2,f f and f (in

canonical sum of products form in decimal notation) are:

( )( )

( )

1

2

, , , 8,9,10

, , , 7,8,12,13,14,15

, , , 8,9

f w x y z

f w x y z

f w x y z

= Σ

= Σ

= Σ

The function 3f is

(a) 9,10Σ (b) 9Σ (c) 1,8,9Σ (d) 8,10,15Σ



6.1 A partial order ≤ is defined on the set 1 2, , , , as n iS x a a a y x a= ≤K for all

1 and for all i, i a y≤ where n ≥1. The number of total orders on the set S which

contain the partial order ≤ is

(a) n! (b) n+2 (c) n (d) 1

6.2 Let G be a graph with 100 vertices numbered 1 to 100. Two vertices i and j are

adjacent if 8 or 12.i j i j− = − = The number of connected components in G is

(a) 8 (b) 4 (c) 12 (d) 25

6.3 The number of equivalence relations of the set 1,2,3,4 is

(a) 15 (b) 16 (c) 24 (d) 4

6.4 Which one of the following regular expressions over 0,1 denotes the set of all

strings not containing 100 as a substring?

(a) 0*(1+0)* (b) 0*1010* (c) 0*1*01 (d) 0(10+1)*

f1

f2

f3=?

f





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6.5 Which one of the following is not decidable?

(a) Given a Turing machine M, a stings s and an integer k, M accepts s within k

steps

(b) Equivalence of two given Turing machines

(c) Language accepted by a given finite state machine is not empty

(d) Language generated by a context free grammar is non empty

6.6 Which of the following language over a,b,c is accepted by a deterministic

pushdown automata?

(a) , *Rw w w a b⊂ ∈ (b) , , *Rww w a b c∈

(c) 0n n na b c n ≥

(d) is a palindrome over , ,w w a b c

Note: wR is the string obtained by reversing ‘w’.

6.7 An operating system contains 3 user processes each requiring 2 units of resource

R. the minimum number of units of r such that no deadlocks will ever arise is

(a) 3 (b) 5 (c) 4 (d) 6

6.8 Each process Pi,i=1……9 is coded as follows

repeat

P(mutex)

critical section

v(mutex)

forever

The code for 10P is identical except that it uses v(mutex) in place of P(mutex).

What is the largest number of processes that can be inside the critical section at any moment?

(a) 1 (b) 2 (c) 3


6.9 For a database relation R(a,b,c,d), where the domains of a, b, c, d include only

atomic values, only the following functional dependencies and those that can be inferred from them hold:

a c

b d

This relation is

(a) in first normal form but not in second normal form

(b) in second normal form but not in third normal form





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(c) in third normal form


6.10 Let R (a, b, c) and S(d, e, f) be two relations in which d is the foreign key of S

that refers to the primary key of R. Consider the following four operations R and S

(a) Insert into R (b) Insert into S

(c) Delete from R (d) Delete from S

Which of the following is true about the referential integrity constraint above?

(a) None of (a), (b), (c) or (d) can cause its violation

(b) All of (a), (b), (c) and (d) can cause its violation

(c) Both (a) and (d) can cause its violation

(d) Both (b) and (c) can cause its violation

7. A D flip-flop is to be connected to an 8085-microprocessor chip as a 1-bit output

port with a port address of FF hex. Data bit D3 should be involved in the data transfer from CPU to the flip-flop. The flip-flop should be cleared on power ON.

(a) Using only one NAND gate (fan in of 10), one NOT gate and one D flip-flop,

draw the required interface logic circuit (only the relevant signals should be shown)

(b) Write a program to generate a squarewave on the output of the flip-flop. ON and OFF periods of the square wave should be 7 bus cycles each.

8. Let L = a1, a2, …….., an) n≥0 be a list whose Pascal representation is

type list = record

next:↑ list; val : integer end

The following function returns a list in which 2ia and 2 1,ia − 1≤i≤2

n

are

interchanged. Complete the function by filling the boxes. Write the line number and the content of the box in your answer sheet.

1. function change (p: ↑ list): ↑ list;

2. var q.t : ↑ list;

3. begin

4. if p = nil then change : = p

5. else if p ↑ next = nil then change :

6. else begin

7. q : p ↑ next;

8. :=q;

9. t : q ↑ next;

10. :=p;

11. :=change(t)

12. end

13. end





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9. Consider a graph whose vertices are points in the plane with integer co-ordinates

(x,y) such that 1≤x≤n and 1≤y≤n, where n≥2 is an integer. Two vertices

( ) ( )1 1 2 2, and ,x y x y are adjacent 1 2 1iff x x− ≤ and 1 2 1y y− ≤ . The weight of

an edge ( ) ( ) ( ) ( )2 2

1 1 2 2 1 2 1 2, , , is x y x y x x y y− + −

(a) What is the weight of a minimum weight-spanning tree in this graph? Write

only the answer without any explanations.

(b) What is the weight of a maximum weight-spanning tree in this graph? Write

only the answer without any explanations?

10. Consider the following program in Pseudo-Pascal syntax.

program what:

var z: integer

procedure recur (x):

begin if x ≤ 40 then

begin x: x + z;

recur (x);

z:=x+10

end

end(*recur*)

begin (*what*)

z =10;

recur(z);

writeln(z)

end

(a) Suppose the parameter to the procedure ‘recur’ is passed by value.

(i) What value is printed by the program?

(ii) How many time is ‘recur’ called?

(b) What value is printed by the program if the parameter is passed by

reference?

11. Consider the grammar

S bSc

S PQR

P bPc

P ε

Q cQd

Q ε

R dRe

R ε





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Where S, P, Q, R are non-terminal symbols with S being the start symbol; b, c, d,

e are terminal symbols and ‘ε’ is the empty string. This grammar generates

strings of the form , , ,i j k mb c d e for some i, j, k, m ≤ 0.

(a) What is the condition on the values of i,j,k,m?

(b) Find the smallest string that has two parse trees.

SECTION – B

Answer any TEN questions from this section. All questions carry equal marks.

12. Consider a hash table with n buckets, where external (overflow) chaining is used

to resolve collisions. The hash function is such that the probability that a key

value is hashed to a particular bucket is 1

.n

The hash table is initially empty and K

distinct values are inserted in the table.

(a) What is the probability that bucket number 1 is empty after the Kth insertion?

(b) What is the probability that no collision has occurred in any of the K

insertisons?

(c) What is the probability that the first collision occurs at the Kth insertions?

13. Let F be the set of one-to-one functions from the set 1,2,…..,n to the set 1,2,…..m where m≥n≥1.

(a) How many functions are members of F?

(b) How many functions f in F satisfy the property f(i)=1 for some i, 1≤i≤n?

(c) How many functions f in F satisfy the property f(i)<f(j) for some 1≤i≤j≤n?

14. Let R be a reflexive and transitive relation on a set A. define a new relation E on

a as

( ) ( ) ( ) , , and ,E a b a b R b a R= ∈ ∈

(a) Prove that E is an equivalence relation on A.

(b) Define a relation ≤ on the equivalence classes of E as E1 ≤ E2 is ∃ a,b such

that 1 2,a E b E∈ ∈ and (a,b)∈R. Prove that ≤ is a partial order.

15. Consider the following function.

Function F(n,m:integer):integer;

begin

If (n <=0) or (m <=0) then F:=1

else

F:F(n - 1,m) + F(n,m – 1);

end;





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Use the recurrence relation 1 1

1

n n n

k k k

− − = +

− to answer the following

questions. Assume that n, m are positive integers. Write only the answers

without any explantion.

(a) What is the value of F(n,2)?

(b) What is the value of F(n,m)?

(c) How many recursive calls are made to the function F, including the original

call, when evaluating F(n,m).

16. A size balanced binary tree is a binary tree in which for every node the difference

between the number of nodes in the left and right subtree is at most 1. The

distance of a node from the root is the length of the path from the root to the

node. The height of a binary tree is the maximum distance of a leaf node from the root.

(a) Prove, by using induction on h, that a size-balance binary tree of height h

contains at least 2h nodes.

(b) In a size-balanced binary tree of height h≤1, how many nodes are at distance

h – 1 from the root? Write only the answer without any explanations.

17. An array A contains n≥1 positive integers in the locatios A[1],A[2],…..,A[n]. the

following program fragment prints the length of a shortest sequence of

consecutive elements of A, A[I],A[i+1],……,A[j]such that the sum of their values

is ≥M, a given positive number. It prints ‘n+1’ if no such sequence exists.

Complete the program by filling the boxes. In each case use the simplest possible expression. Write only the line number and the contents of the box.

1. begin

2. i :+1;j:=1;

3. Sum := ;

4. min:n; finish:= false;

5. While not finish do

6. If then

7. if j = n then finish:=true.

8. else

9. begin

10. j:=j+1;

11. sum:=

12. end

13. else

14. begin

15. If(j – I) < min then min:=j – 1;

16. sum:=sum – A[i];

17. i:=i+1;





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18. end

19. writeln (min +1);

20. end.

18. Consider the following piece of ‘C’ code fragment that removes duplicates from

an ordered list of integers.

struct node

int val;

struct nod *next;

;

typedef struct node Node;

Node *remove-duplicates (Node*head, int *j)

Node *t1, *t2;

*j=0;

t1 = head;

if (t1! = NULL) t2 = t1 next;

else return head:

*j = 1;

if (t2 == NULL) return head;

while t2 ! = NULL)

if (t1.val! = t2.val) ------------------ (S1)

(*j)++; t1 next = t2; t1 = t2: -----------(S2)

t2 = t2 next;

t1 next =NULL;

return head;

Assume the list contains n elements (n – 2) in the following questions.

(a) How many times is the comparison in statements S1 made?

(b) What is the minimum and the maximum number of times statements marked

S2 get executed?

(c) What is the significance of the value in the integer pointed to by j when the

function completes?





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19. A B+ - tree of order d is a tree in which each internal node has between d and 2 d

key values. An internal node with M key values M + 1 children. The root (if it is

an internal node) has between 1 and 2d key values. The distance of a node from

the root is the length of the path from the root to the node. All leaves are at the

same distance from the root. The height of the tree is the distance of a leaf fro the root.

(a) What is the total number of key values in the internal nodes of a B+ - tree

with 1 leaves (1 ≥ 2)?

(b) What is the maximum number of internal nodes in a B+-tree of order 4 with

52 leaves?

(c) What is the minimum number of leaves in a B+-tree of order d and height

h(n≥1)?

20. Construct a finite state machine with minimum number of states, accepting all

strings over (a,b) such that the number of a’s is divisible by two and the number of b’s is divisible by three.

21. Given that L is a language accepted by a finite state machine, show that

and P RL L are also accepted by some finite state machines, where

some string. s' .PL s ss L′= ∈

obtainable by reversing some string in L .PL s s=

22. A language L is a subset of Pascal with the following constructs:

(a) Expressions involving the operators ‘+’ and ‘<’ only

(b) Assignment statements

(c) ‘while’ statements and

(d) Compound statements with the syntax ‘begin…end’

Give an unambiguous grammar of L.

23. The language L, defined by the following grammar, allows use of real or integer

data in expressions and assignment statements.

( )( )

assign-stmt :: :

::

:: *

::

::

LHS E

E E T T

T T V V

V id E

LHS id

=

= +

=

=

It is required to convert expression and assignment strings of L into postfix

strings that use the type-specific operations (+,i) (+,r), (*,i), (*,r), (:=,i) and

(:=,r)





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Write a syntax directed translation scheme to convert expression and assignment

strings into the post-fix form. You may assume that the name and type of a

variable can be obtained by making the function calls’ give type (id) and give-name (id)* respectively.

24. Consider the following program fragment in Pascal:

Program Main;

var X: integer;

procedure A;

var Y: integer;

procedure B;

var Z: integer;

procedure C;

var Z: integer;

begin (*procedure C*)

:

end (*procedure C*)

begin (*procedure B*)

:

C; (*call to C*)

A; (*call to A*)

:

end (*procedure B*)

begin (* procedure A*)

:

B; (*call to B*)

:

end (*procedure A*)

begin (*Main*)





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SECTION - A

1. This question consists of 35 THIRTY-FIVE multiple questions of ONE mark each.

For each question, four possible alternatives (A, B, C and D) are given, out of

which ONLY ONE is correct. Indicate the correct answer in the boxes

corresponding to the questions only on the FIRST sheet of the answer book.

1.1 A die is rolled three times. The probability that exactly one odd number turns up

among the three outcomes is

(a) 1

6 (b)

3

8 (c)

1

8 (d)

1

2

1.2 Consider the following set of equations:

2 5

4 8 12

3 6 3 15

x y

x y

x y z

+ =

+ =

+ + =

This set

(a) has unique solution (b) has no solutions

(c) has finite number of solutions (d) has infinite number of solutions

1.3 Which of the following statements applies to the bisection method used for

finding roots of functions:

(a) converges within a few iterations

(b) guaranteed to work for all continuous functions

(c) is faster than the Newton-Raphson method

(d) requires that there be no error in determining the sign of the function.

1.4 Consider the function y x= in the interval [-1,1]. In this interval, the function is

(a) continuous and differentiable

(b) continuous but not differentiable

(c) differentiable but not continuous

(d) neither continuous nor differentiable

1.5 What is the converse of the following assertion?

I stay only if you go

(a) I stay if you go

(b) If I stay then you go

(c) If you do not go then I do not stay

(d) If I do not stay then you go





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1.6 Suppose A is a finite set with n elements. The number of elements in the largest equivalence relation of A is

(a) n (b) 2n (c) 1 (d) n + 1

1.7 Let R1 and R2 be two equivalence relations on a set. Consider the following assertions:

(i) 1 2R R∪ is an equivalence relation

(ii) 1 2R R∩ is an equivalence relation

Which of the following is correct?

(a) Both assertions are true

(b) Assertion (i) is true but assertion (ii) is not true

(c) Assertion (ii) is true but assertion (i) is not true

(d) Neither (i) nor (ii) is true

1.8 The number of functions from an m element set to an n element set is

(a) m + n (b) nm (c) mn (d) m*n

1.9 If the regular set A is represented by A = (01 + 1)* and the regular set ‘B’ is

represented by B = ((01)*1*)*, which of the following is true?

(a) A ⊂ B (b) B ⊂ A

(c) A and B are incomparable (d) A = B

1.10 Which of the following set can be recognized by a Deterministic Finite state

Automaton?

(a) The numbers 1, 2, 4, 8, ……………. 2n , ………… written in binary

(b) The numbers 1, 2, 4, ……………….,2n , …………..written in unary

(c) The set of binary string in which the number of zeros is the same as the

number of ones.

(d) The set 1, 101, 11011, 1110111, ………..

1.11 Regarding the power of recognition of languages, which of the following

statements is false?

(a) The non-deterministic finite-state automata are equivalent to deterministic

finite-state automata.

(b) Non-deterministic Push-down automata are equivalent to deterministic Push-

down automata.

(c) Non-deterministic Turing machines are equivalent to deterministic Push-down automata.

(d) Non-deterministic Turing machines are equivalent to deterministic Turing

machines.

(e) Multi-tape Turing machines are equivalent to Single-tape Turing machines.





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1.12 The string 1101 does not belong to the set represented by

(a) 110*(0 + 1) (b) 1 ( 0 + 1)* 101

(c) (10)* (01)* (00 + 11)* (d) (00 + (11)*0)*

1.13 What happens when a bit-string is XORed with itself n-times as shown:

((( timesB B B B n ⊕ ⊕ ⊕ K

(a) complements when n is even (b) complements when n is odd

(c) divides by 2n always

(d) remains unchanged when n is even

1.14 A multiplexor with a 4 bit data select input is a

(a) 4:1 multiplexor (b) 2:1 multiplexor

(c) 16:1 multiplexor (d) 8:1 multiplexor

1.15 The threshold level for logic 1 in the TTL family is

(a) any voltage above 2.5 V

(b) any voltage between 0.8 V and 5.0 V

(c) any voltage below 5.0 V

(d) any voltage below ccV but above 2.8 V

1.16 In serial communication employing 8 data bits, a parity bit and 2 stop bits, the

minimum band rate required to sustain a transfer rate of 300 characters per second is

(a) 2400 band (b) 19200 band

(c) 4800 band (d) 1200 band

1.17 The octal representation of an integer is 3428. If this were to be treated as an

eight-bit integer is an 8085 based computer, its decimal equivalent is

(a) 226 (b) -98 (c) 76 (d) -30

1.18 Which of the following devices should get higher priority in assigning interrupts?

(a) Hard disk (b) Printer

(c) Keyboard (d) Floppy disk

1.19 Which of the following addressing modes permits relocation without any change whatsoever in the code?

(a) Indirect addressing (b) Indexed addressing

(c) Base register addressing (d) PC relative addressing





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1.20 Which of the following is true?

(a) Unless enabled, a CPU will not be able to process interrupts.

(b) Loop instructions cannot be interrupted till they complete.

(c) A processor checks for interrupts before executing a new instruction.

(d) Only level triggered interrupts are possible on microprocessors

1.21 Which one of the following algorithm design techniques is used in finding all pairs

of shortest distances in a graph?

(a) Dynamic programming (b) Backtracking

(c) Greedy (d) Divide and Conquer

1.22 Give the correct matching for the following pairs:

(a) A – R B – P C – Q D - S (b) A – R B – P C – S D - Q

(c) A – P B – R C – S D - Q (d) A – P B – S C – R D - Q

1.23 How many sub strings of different lengths (non-zero) can be found formed from a

character string of length n?

(a) n (b) 2n (c) 2n (d) ( )1

2

n n +


(a) A tree with a n nodes has (n – 1) edges

(b) A labeled rooted binary tree can be uniquely constructed given its postorder

and preorder traversal results.

(c) A complete binary tree with n internal nodes has (n + 1) leaves.

(d) The maximum number of nodes in a binary tree of height h is ( )12 1h+ −

1.25 In a resident – OS computer, which of the following systems must reside in the

main memory under all situations?

(a) Assembler (b) Linker

(c) Loader (d) Compiler

(A) O (log n) (P) Selection

(B) O (n) (Q) Insertion sort

(C) O (n log n) (R) Binary search

(D) O ( )2n (S) Merge sort





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1.26 Which of the following statements is true?

(a) SLR parser is more powerful than LALR

(b) LALR parser is more powerful than Canonical LR parser

(c) Canonical LR parser is more powerful than LALR parser.

(d) The parsers SLR, Canonical CR, and LALR have the same power

1.27 Type checking is normally done during

(a) lexical analysis (b) syntax analysis

(c) syntax directed translation (d) code optimization

1.28 A linker reads four modules whose lengths are 200, 800, 600 and 500 words,

respectively. If they are loaded in that order, what are the relocation constants?

(a) 0, 200, 500, 600 (b) 0, 200, 1000, 1600

(c) 200, 500, 600, 800 (d) 200, 700, 1300, 2100

1.29 Which of the following is an example of a spooled device?

(a) The terminal used to enter the input data for the C program being executed

(b) An output device used to print the output of a number of jobs.

(c) The secondary memory device in a virtual storage system

(d) The swapping area on a disk used by the swapper.

1.30 When the result of a computation depends on the speed of the processes

involved there is said to be

(a) cycle steating (b) rare condition

(c) a time lock (d) a deadlock

1.31 A counting semaphore was initialized to 10. Then 6 P (wait) operations and 4V

(signal) operations were completed on this semaphore. The resulting value of the

semaphore is

(a) 0 (b) 8 (c) 10 (d) 12

1.32 A computer has six tape drives, with n processes competing for them. Each

process may need two drives. What is the maximum value of n for the system to be deadlock free?

(a) 6 (b) 5 (c) 4 (d) 3

1.33 Given two union compatible relations R1(A,B) and R2 (C,D), what is the result of

the operation R1A = CAB = DR2?

(a) 1 2R R∪ (b) 1 2R R× (c) 1 2R R− (d) 1 2R R∩





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1.34 Which normal form is considered adequate for normal relational database design?

(a) 2 NF (b) 5 NF (c) 4 NF (d) 3 NF

1.35 There are five records in a database.

Name Age Occupation Category

Rama 27 CON A

Abdul 22 ENG A

Jeniffer 28 DOC B

Maya 32 SER D

Dev 24 MUS C

There is an index file associated with this and it contains the values 1,3,2,5 and

4.Which one of the fields is the index built from?

(a) Age (b) Name (c) Occupation (d) Category

2. This question consists of 20 (TWENTY) multiple-choice questions (2.1 – 2.20) of

TWO marks each. The answers to the multiple choice questions of this section

MUST be written only in the boxes corresponding to the questions, in the second

page of the answer book.

2.1 The rank of the matrix given below is:

1 4 8 7

0 0 3 0

4 2 3 1

3 12 24 2

(a) 3 (b) 1 (c) 2 (d) 4

2.2. Consider the following determinant

1

1

1

a bc

b ca

C ab

∆ = .

Which of the following is a factor of ∆ ?

(a) a+b (b) a-b (c) a+b+c (d) abc





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2.3. The binary relation ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )1,1 , 2,1 , 2,2 , 2,3 , 2,4 , 3,1 , 3,2 , 3,3 , 3,4R = on

the set A = 1,2,3,4 is

(a) reflexive, symmetric and transitive

(b) neither reflexive, nor irreflexive but transitive

(c) irreflexive, symmetric and transitive

(d) irreflexive and antisymmetric

2.4. In a room containing 28 people, there are 18 people who speak English, 15

people who speak Hindi and 22 people who speak Kannada. 9 persons speak both

English and Hindi, 11 persons speak both Hindi and Kannada whereas 13 persons speak both Kannada and English. How many people speak all three languages?

(a) 9 (b) 8 (c) 7 (d) 6

2.5. Let L be the set of all binary strings whose last two symbols are the same. The

number of states in the minimum state deterministic finite 0 state automaton

accepting L is

(a) 2 (b) 5 (c) 8 (d) 3

2.6. Which of the following statements is false?

(a) Every finite subset of a non-regular set is regular

(b) Every subset of a regular set is regular

(c) Every finite subset of a regular set is regular

(d) The intersection of two regular sets is regular

2.7. The function represented by the Karnaugh map given below is

(a) A.B (b) AB+BC+CA (c) B C⊕ (d) A.BC

2.8. Which of the following operations is commutative but not associative?

(a) AND (b) OR (c) NAND (d) EXOR

2.9. Formatting for a floppy disk refers to

(a) arranging the data on the disk in contiguous fashion

(b) writing the directory

(c) erasing the system area

(d) writing identification information on all tracks and sectors

BC A

1 1 0 1

1 0 0 1

0

1

00 01 10 11





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2.10. The address space of 8086 CPU is

(a) one Megabyte (b) 256 Kilobytes

(c) 1 K Megabytes (d) 64 Kilobytes

2.11. A complete n-ary tree is one in which every node has O or n sons. If x is the

number of internal nodes of a complete n-ary tree, the number of leaves in it is given by

(a) x(n – 1) +1 (b) xn - 1 (c) xn + 1 (d) x(n+1)

2.12. What value would the following function return for the input x = 95?

Function fun (x:integer):integer;

Begin

If x > 100 then fun : x – 10

Else fun : fun(fun (x + 11))

End;

(a) 89 (b) 90 (c) 91 (d) 92

2.13. What is the result of the following program?

program side-effect (input, output);

var x, result: integer:

fucntion f (var x:integer):integer;

begin

x:x+1;f:=x;

end

begin

x:=5

result:=f(x)*f(x)

writeln(result)

end

(a) 5 (b) 25 (c) 36 (d) 42

2.14. Let A be a two-dimensional array declared as follows:

A: array [1 …. 10] [1 …… 15] of integer;

Assuming that each integer takes one memory locations the array is stored in

row-major order and the first element of the array is stored at location 100, what

is the address of the element A[i][j]?

(a) 15i + j + 84 (b) 15j + i + 84

(c) 10i + j + 89 (d) 10j + i + 89





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2.15. Faster access to non-local variables is achieved using an array of pointers to

activation records called a

(a) stack (b) heap

(c) display (d) activation tree

2.16. The overlay tree for a program is as shown below:

What will be the size of the partition (in physical memory) required to load (and

run) this program?

(a) 12 KB (b) 14 KB (c) 10 KB (d) 8 KB

2.17. Consider n processes sharing the CPU in a round-robin fashion. Assuming that

each process switch takes s seconds, what must be the quantum size q such that

the overhead resulting from process switching is minimized but at the same time

each process is guaranteed to get its turn at the CPU at least every t seconds?

(a) 1

t nsq

n

−≤

− (b)

1

t nsq

n

−≥

− (c)

1

t nsq

n

−≤

+ (d)

1

t nsq

n

−≥

+

2.18. If an instruction takes i microseconds and a page fault takes an additional j

microseconds, the effective instruction time if on the average a page fault occurs

every k instruction is:

(a) j

ik

+ (b) *i j k+ (c) i j

k

+ (d) ( ) *i j k+

2.19. Which of the following query transformations (i.e. replacing the l.h.s. expression

by the r.h.s. expression) is incorrect? R1 and R2 are relations, C1, C2 are selection conditions and A1, A2 are attributes of R1?

(a) ( )( ) ( )( )1 1 1 2 2 1c c c cR Rσ σ σ σ→ (b) ( )( ) ( )( )1 1 1 1 1 1c A A cR Rσ π π σ→

(c) ( ) ( ) ( )1 1 2 1 1 1 2c c cR R R Rσ σ σ∪ → ∪ (d) ( )( ) ( )( )1 1 1 1 1 1A c c AR Rπ σ σ π→

A B C

D E F G

4 KB 6 KB 8 KB

4 KB 2 KB 8 KB 6 KB

2 KB Root





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2.20. Suppose the domain set of an attribute consists of signed four digit numbers.

What is the percentage of reduction in storage space of this attribute if it is stored as an integer rather than in character form?

(a) 80% (b) 20% (c) 60% (d) 40%

3. (a) Two friends agree to meet at a park with the following conditions. Each will

reach the park between 4.0 p.m. and 5.00 p.m. and will see if the other has

already arrived. If not, they will wait for 10 minutes or the end of the hour

whichever is earlier and leave. What is the probability that the two will not meet?

(b) Give a regular expression for the set of binary strings where 0 every is

immediately followed by exactly k 1’s and preceded by at least k 1’s (k is a fixed integer)

4. Design a deterministic finite state automaton (using minimum number of states)

that recognizes the following language:

L = w ∈ 0, 1*|w interpreted as binary number (ignoring the leading zeros) is

divisible by five.

5. (a) The implication gate, shown below has two inputs (x and y); the output is 1

except when x = 1 and y = 0, realize f = xy xy+ using only four implication

gates.

(b) show that the implication gate is functionally complete.

6. (a) Solve the following recurrence relation

1

1

2 1, 1

2

n nx x n

x

−= − >

=

(b) Consider the grammar

S Aa|b

A Ac|Sd|∈

Construct an equivalent grammar with no left recursion and with minimum

number of production sales.

7. (a) Suppose we have a database consisting of the following three relations.

FREQUENTS (student, parlor) giving the parlors each student visits.

SERVES (parlor, ice-cream) indicating what kind of ice-creams each parlor

serves.

LIKES (student, ice-cream) indicating what ice-creams each student likes.

(Assume that each student likes at least one ice-cream and frequents at least

one parlor)

Express the following in SQL:





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Print the students that frequent at least one parlor that serves some ice-

cream that they like.

(b) In a computer system where the ‘best-fit’ algorithm is used for allocating

‘jobs’ to ‘memory partitions’, the following situation was encountered:

Partitions sizes in KB 4K 8K 20K 2K

Jobs sizes in KB 2K 14K 3K 6K 6K 10K 20K 2K

Time for execution 4 10 2 1 4 1 8 6

When will the 20K job complete?

SECTION – B

This section consists of TWENTY questions numbered 8 to 27 of FIVE marks each.

Attempt ANY TEN questions. Answers must be given in the answer book provided.

Answer for each question must start on a fresh page and must appear at one place only. (Answers to all parts of a question must appear together).

8. (a) Find the points of local maxima and minima, if any, of the following function

defined in 0≤x≤6.

3 26 9 15x x x− + +

(b) Integrate

cosx xdxπ

π−∫

9. Derive the expression for the number of operations required to solve a system of

linear equations in n unknowns using the Gaussian Elimination Method. Assume that one operation refers to a multiplication followed by an addition.

10. (a) Prove by induction that the expression for the number of diagonals in a

polygon of n sides is ( )3

2

n n −

(b) Let R be a binary relation on A = a, b, c, d, e, f, g, h represented by the

following two component digraph. Find the smallest integers m and n such that m < n and Rm = Rn.

a

b

c

d

e

f

g h





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11. Suppose A = a,b,c,d and 1Π is the following partition of A

1Π =a,b,cd

(a) List the ordered pairs of the equivalence relations induced by 1Π .

(b) Draw the graph of the above equivalence relation.

(c) Let 2 , , ,a b C dΠ =

3 , , ,a b c dΠ =

and 4 , ,a b c dΠ =

Draw a Poset diagram of the poset,

1 2 3 4, , , , refinesΠ Π Π Π

12. Let (A, *) be a semigroup, Furthermore, for every a and b in A, if a ≠ b, then a*b,

b ≠ b*a.

(a) Show that for every a in A

a*a =a

(b) Show that for every a, b in A

a*b*a =a

(c) Show that for every a, b, c in A

a*b*c = a*c

13. Let ( )0 1 0 0 0, , 0,1 , , , , , ,M q q z X q zδ φ= be a Pushdown automation where δ is

given by

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

0 0 0 0

0 0 0

0 0

1 1

0 1

0 0 0 0

,1, ,

, , ,

,1, ,

,1, ,

,0, ,

,0, ,

q z q xz

q z q

q X q XX

q X q

q X q X

q z q z

δ

δ

δ

δ

δ

δ

=

∈ = ∈

=

= ∈

=

=

(a) What is the language accepted by this PDA by empty store?

(b) Describe informally the working of the PDA.

14. (a) Let G1 = (N, T, P, S1) be a CFG where,

N = S1, A, B T = a, b and

P is given by





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S1 a, S1 b S1 a B b

S1 a A b B Bb

A a A B b

A a

What is L(G1)?

(b) Use the grammar in Part (a) to give a CFG

for ( )12 , , .1 1, or 1i i kL a b a b i j k i j k= ≥ = = by adding not more than 5

production rules.

(c) Is L2 inherently ambiguous?

15. (a) Draw the schematic of 8085 based system that can be used to measure the

width of a pulse. Assume that the pulse is given as a TTL compatible signal

by the source, which generates it.

(b) Write the 8085 Assembly Language program to measure the width of the

pulse. State all your assumptions clearly.

16. Design a synchronous counter to go through the following states:

1, 4, 2, 3, 1, 4, 2, 3, 1, 4 ……………

17. Calculate the total time required to read 35 sectors on a 2-sided floppy disk.

Assume that each track has 8 sectors and the track-to-track step time is 8

milliseconds. The first sector to be read is sector 3 on track 10. Assume that the

diskette is soft sectored and the controller has a 1-sector buffer. The diskette

spins at 300 RPM and initially; the head is on track 10.

18. For a set-associative Cache Organization, the parameters are as follows:

tc -- Cache access time

tm -- Main memory access time

l -- number of sets

b -- block size

k * b -- set size

Calculate the hit ratio for a loop executed 100 times where the size of the loop is

n * b, and n = k*m is a non-zero integer and 1 < m ≤ 1.

Give the value of the hit ratio for 1 = 1





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19. (a) Let p be a pointer as shown in the figure in a single linked list.

What do the following assignment statements achieve?

q: = p next

p next:=q next

p next:=(q next) next

(p next) next:=q

(b) Compute the post fix equivalent of the following expression.

( )3 * log 12

ax + −

20. Draw the binary tree with node labels a, b, c, d, e, f and g for which the inorder

and postorder traversals result in the following sequences.

Inorder a f b c d g e

Postorder a f c g e d b

21. (a) Derive a recurrence relation for the size of the smallest AVL tree with height

h.

(b) What is the size of the smallest AVL tree with height 8?

(c)

22. (a) An identifier in a programming language consists of up to six letters and

digits of which the first character must be a letter. Derive a regular expression for the identifier.

(b) Build an LL (1) parsing table for the language defined by the LL(1) grammar

with productions

Program begin d semi X end

X d semi X | sY

Y semi s Y | ∈

23. Let the attribute ‘val’ give the value of a binary number generated by S in the

following grammar:

S L.L | L

L LB | B

B 0 | 1

For example, an input 101.101 give S.val = 5.625

Construct a syntax directed translation scheme using only synthesized attributes,

to determine S.val.

p cell i cell(i+1) cell(i+2) cell(i+3)

…………. ………….





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24. (a) Four jobs are waiting to be run. Their expected run times are 6, 3, 5 and x.

in what order should they be run to minimize the average response time?

(b) Write a concurrent program using par begin-par end to represent the

procedure graph shown below.

25. (a) Free disk space can be kept track of using a free list or a bit map. Disk

addresses require d bits. For a disk with B blocks, F of which are free, state the condition under which the free list uses less space than the bit map.

(b) Consider a disk with C cylinders, t tracks per cylinder, s sectors per track and

a sector length sl. A logical file dl with fixed record length rl is stored

continuously on this disk starting at location (cL,tL,sL), when CL, tL and SL are

the cylinder, track and sector numbers, respectively. Derive the formula to

calculate the disk address (i.e. cylinder, track and sector) of a logical record n assuming that rl = sl.

26. Consider the following database relations containing the attributes

Book – id

Subject – Category – of – book

Name – of – Author

Nationality – of – Author

With book – id as the primary key.

(a) What is the highest normal form satisfied by this relation?

(b) Suppose the attributes Book – title and Author – address are added to the

relation, and the primary key is changed to Name – of – Author, Book – title, what will be the highest normal form satisfied by the relation?

27. Consider the following relational database schemes:

COURSES (Cno.name)

PRE-REQ(Cno, pre-Cno)

COMPLETED (student – no, Cno)

COURSES gives the number and name of all the available courses.

PRE-REQ gives the information about which courses are pre-requisites for a given

course.

COMPLETED indicates what courses have been completed by students.

Express the following using relational algebra:

List all the courses for which a student with student-no 2310 has completed all

the pre-requisites.

S1

S2 S3

S4

S5





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SECTION - A

1. This question consists of TWENTY-FIVE multiple questions of ONE mark each. For

each question, four possible alternatives (A, B, C and D) are given, out of which

ONLY ONE is correct. Indicate the correct answer in the boxes corresponding to

the questions only on the FIRST sheet of the answer book.

1.1 Suppose that the expectation of a random variable X is 5. Which of the following

statements is true?

(a) There is a sample point at which X has the value 5.

(b) There is a sample point at which X has value greater than 5.

(c) There is a sample point at which X has a value greater than or equal to 5.


1.2 The number of binary relations on a set with n elements is:

(a) 2n (b) 2n

(c) 2

2n (d) None of the above

1.3 The number of binary strings of n zeroes and k ones that no two ones are

adjacent is

(a) 1nkC− (b) n

kC

(c) 1n

kC + (d) None of the above

1.4 Consider the regular expression (0 + 1) (0 + 1)…. N times. The minimum state

finite automation that recognizes the language represented by this regular

expression contains

(a) n states (b) n + 1 states

(c) n + 2 states (d) None of the above

1.5 Context-free languages are closed under:

(a) Union, intersection (b) Union, Kleene closure

(c) Intersection, complement (d) Complement, Kleene closure

1.6 Let LD be the set of all languages accepted by a PDA by final state and LE the set

of all languages accepted by empty stack. Which of the following is true?

(a) LD = LE (b) LD ⊃ LE

(c) LE = LD (d) None of the above

1.7 Which of the following expressions is not equivalent to x ?

(a) x NAND X (b) x NOR x (c) x NAND 1 (d) x NOR 1





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1.8 Which of the following functions implements the Karnaugh map shown below?

CD

AB 00 00 11 10

00 0 0 1 0

01 X X 1 X

11 0 1 1 0

10 0 1 1 0

(a) AB CD+ (b) D(C +A)

(c) AD + AB (d) ( ) ( ) ( )C D C D A B+ + + +

1.9 Listed below are some operating system abstractions (in the left column) and the

hardware components (in the right column)?

(a) (A) – 2 (B) – 4 (C) – 3 (D) - 1 (b) (A) – 1 (B) – 2 (C) – 3 (D) – 4

(c) (A) – 3 (B) – 2 (C) – 4 (D) - 1 (d) (A) – 4 (B) – 1 (C) – 2 (D) – 3

1.10 Which of the following disk scheduling strategies is likely to give the best through

put?

(a) Farthest cylinder next (b) Nearest cylinder next

(c) First come first served (d) Elevator algorithm

1.11 System calls are usually invoked by using

(a) a software interrupt (b) polling

(c) an indirect jump (d) a privileged instruction

1.12 A sorting technique is called stable if

(a) it takes O (nlog n) time

(b) it maintains the relative order of occurrence of non-distinct elements

(c) it uses divide and conquer paradigm

(d) it takes O(n) space

(A) Thread 1. Interrupt

(B) Virtual address space 2. Memory

(C) File system 3. CPU

(D) Signal 4. Disk





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1.13 Suppose we want to arrange the n numbers stored in any array such that all

negative values occur before all positive ones. Minimum number of exchanges required in the worst case is

(a) n - 1 (b) n

(c) n + 1 (d) None of the above

1.14 If one uses straight two-way merge sort algorithm to sort the following elements

in ascending order:

20, 47, 15, 8, 9, 4, 40, 30, 12, 17

then the order of these elements after second pass of the algorithm is:

(a) 8, 9, 15, 20, 47, 4, 12, 17, 30, 40

(b) 8, 15, 20, 47, 4, 9, 30, 40, 12, 17

(c) 15, 20, 47, 4, 8, 9, 12, 30, 40, 17

(d) 4, 8, 9, 15, 20, 47, 12, 17, 30, 40

1.15 The number of articulation points of the following graph is

(a) 0 (b) 1 (c) 2 (d) 3

1.16 If n is a power of 2, then the minimum number of multiplications needed to

compute a* is

(a) log2n (b) n (c) n -1 (d) n

1.17 Which of the following is the most powerful parsing method?

(a) LL (1) (b) Canonical LR (c) SLR (d) LALR

1.18 Consider the join of a relation R with a relation S. If R has m tuples and S has n

tuples then the maximum and minimum sizes of the join respectively are

(a) m + n and 0 (b) mn and 0

(c) m + n and |m – n| (d) mn and m + n

1

2 3

4

5

6

7





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1.19. The relational algebra expression equivalent to the following tuple calculus expression:

( ) 10 20t t r t A t B∈ ∧ = ∧ = is

(a) ( ) ( )10 20A Brσ

= ∨ = (b) ( ) ( ) ( ) ( )10 20A B

r rσ σ= =

∪

(c) ( ) ( ) ( ) ( )10 20A Br rσ σ

= =∩ (d) ( ) ( ) ( ) ( )10 20A B

r rσ σ= =

−

1.20. Booth’s coding in 8 bits for the decimal number –57 is

(a) 0 – 100 + 1000 (b) 0 – 100 + 100 -1

(c) 0 – 1 + 100 – 10 + 1 (d) 0 0 – 10 + 100 - 1

1.21. The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit number is

(a) O ( )2n (b) O(n) (c) O(log n) (d) O(1)

1.22. The main memory of a computer has 2 cm blocks while the cache has 2 c blocks.

If the cache uses the set associative mapping scheme with 2 blocks per set, then

block k of the main memory maps to the set

(a) (k mod m) of the cache (b) (k mod c) of the cache

(c) (k mod 2c) of the cache (d) (k mod 2 cm) of the cache

1.23. The Newton-Raphson method is to be used to find the root of the equation f(x)=0

where ox is the initial approximation and f ′ is the derivative of f. The method

converges

(a) always (b) only if f is a polynomial

(c) only if ( ) 0of x < (d) None of the above

1.24. Let R = (a, b, c, d, e, f) be a relation scheme with the following dependencies

c f, e a, ec d. a b. Which of the following is a key for R?

(a) CD (b) EC (c) AE (d) AC

1.25 Which of the following is correct?

(a) B-trees are for storing data on disk and B+ trees are for main memory.

(b) Range queries are faster on B* trees.

(c) B-trees are for primary indexes and B* trees are for secondary indexes.

(d) The height of a B* tree is independent of the number of records.





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2. This question consists of TWENTY-FIVE sub-questions, of TWO marks each. For

each of these sub-questions, four possible alternatives (A, B, C and D) are given,

out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the SECOND sheet of the answer book.

2.1 Consider two events E1 and E2 such that probability of E1, Pr [E1]= 1,

2probability

of E2, Pr 21

1,

3E = and probability of E1 and E2, Pr[E1 and E2]=

1.

5 Which of the

following statements is/are true?

(a) 1 2

2Pr or is

3E E

(b) Events E1 and E2 are independent

(c) Events E1 and E2 are not independent

(d) 1

2

4Pr

5

E

E

=

2.2. Two girls have picked 10 roses, 15 sunflowers and 15 daffodils. What is the number of ways they can divide the flowers amongst themselves?

(a) 1638 (b) 2100


2.3. Let L be a set with a relation R which is transitive, anti-symmetric and reflexive

and for any two elements a, b ∈ L let the least upper bound lub (a,b) and the

greatest lower bound glb (a,b) exist. Which of the following is/are true?

(a) L is a poset (b) L is a Boolean algebra

(c) -L1 is context free (d) -L2 is regular

2.4. If L is context free language and L2 is a regular language which of the following

is/are false?

(a) L1 – L2 is not context free (b) L1 ∩ L2 is context free

(c) ~L1 is context free (d) ~L2 is regular

2.5. Given the programming constructs (i) assignment (ii) for loops where the loop

parameter cannot be changed within the loop (iii) if-then-else (iv) forward go to

(v) arbitrary go to (vi) non-recursive procedure call (vii) recursive

procedure/function call (viii) repeat loop, which constructs will you not include in

a programming language such that it should be possible to program the

terminates (i.e., halting) function in the same programming language.

(a) (ii), (iii), (iv)

(b) (v), (vii), (viii)

(c) (vi), (vii), (viii)

(d) (iii), (vii), (viii)





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2.6. For the schedule given below, which of the following is correct:

1 Read

2 Read B

3 Write A

4 Read A

5 Write A

6 Write B

7 Read B

8 Write B

(a) This schedule is serialized and can occur in a scheme using 2PL protocol

(b) This schedule is serializable but cannot occur in a scheme using 2PL protocol

(c) This schedule is not serialiable but can occur in a scheme using 2PL protocol

(d) This schedule is not seralisable and cannot occur in a scheme using 2PL

protocol.

2.7. Consider the schema R = (S T U V) and the dependencies S T, T U. U V

and V S. Let R = (R1 and R2) be a decomposition such that R1 ∩ R2 = ∅ . The

decomposition is

(a) not in 2NF (b) in 2NF but not 3NF

(c) in 3NF but not in 2NF (d) in both 2NF and 3NF

2.8. Consider the circuit shown below. In a certain steady state, the line Y is at ‘1’.

What are the possible values of A, B and c in this state?

(a) A = 0, B = 0, C = 1 (b) A = 0, B = 1, C = 1

(c) A = 1, B = 0, C = 1 (d) A = 1, B = 1, C = 1

2.9. Which of the following sets of component(s) is/are sufficient to implement any

arbitrary Boolean function?

(a) XOR gates, NOT gates

(b) 2 to 1 multiplexors

(c) AND gates, XOR gates

(d) Three-input gates that output (A.B) + C for the inputs A. B and C.

A

B

C

Y





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2.10. A multi-user, multi-processing operating system cannot be implemented on

hardware that does not support

(a) Address translation

(b) DMA for disk transfer

(c) At least two modes of CPU execution (privileged and non-privileged)

(d) Demand paging

2.11. Which of the following is/are advantage of virtual memory?

(a) Faster access to memory on an average.

(b) Processes can be given protected address spaces.

(c) Linker can assign addresses independent of where the program will be loaded

in physical memory.

(d) Programs larger than the physical memory size can be run.

2.12. Which of the following actions is/are typically not performed by the operating

system when switching context from process A to process B?

(a) Saving current register values and restoring saved register values for process

B.

(b) Changing address translation tables.

(c) Swapping out the memory image of process A to the disk.

(d) Invalidating the translation look-aside buffer.

2.13. Consider the following program in a language that has dynamic scooping:

var x: real;

procedure show:

begin print(x);end;

procedure small;

var x: real;

begin x: = 0.125; show; end;

begin x:=0.25;

show; small

end.

Then the output of the program is:

(a) 0.125 0.125 (b) 0.25 0.25 (c) 0.25 0.125 (d) 0.125 0.25

2.14. The number of tokens in the Fortran statement DO 10 I = 1.25 is

(a) 3 (b) 4






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2.15. A grammar that is both left and right recursive for a non-terminal, is

(a) Ambiguous (b) Unambiguous

(c) Information is not sufficient to decide whether it is ambiguous or

unambiguous


2.16. The number of full and half-adders required to add 16-bit numbers is

(a) 8 half-adders, 8 full-adders (b) 1 half-adder, 15 full-adders

(c) 16 half-adders, 0 full-adders (d) 4 half-adders, 12 full-adders

2.17. Zero has two representations in

(a) Sign magnitude (b) 1’s complement

(c) 2’s complement (d) None of the above

2.18. Raid configurations of the disks are used to provide

(a) Fault-tolerance (b) High speed

(c) high data density (d) None of the above

2.19. Arrange the following configuration for CPU in decreasing order of operating

speeds: Hard wired control, vertical microprogramming, horizontal

microprogramming.

(a) Hard wired control, vertical micro-programming, horizontal micro-

programming.

(b) Hard wired control, horizontal micro-programming, vertical micro-

programming.

(c) horizontal micro-programming, vertical micro-programming, Hard wired control.

(d) vertical micro-programming, horizontal micro-programming, hard wired

control.

2.20. The minimum number of record movements required to merge five files A (with

10 records), B (with 20 records), C (with 15 records), D (with 5 records) and E (with 25 records) is:

(a) 165 (b) 90 (c) 75 (d) 65

2.21. If T1 = O(1), give the correct matching for the following pairs:

(M) 1n nT T n−= + (U) ( )nT O n=

(N)

2

n nT T n= + (V) ( )lognT O n n=

(O)

2

logn nT T n n= + (W) ( )2nT O n=

(P) 1 logn nT T n−= + (X) ( )2lognT O n=





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(a) M – W N – V O – U P - X (b) M – W N – U O – X P - V

(c) M – V N – W O – X P - U (d) M – W N – U O – V P - X

2.22. The main differences(s) between a CSIC and A RISC processor is/are that a RISC

processor typically

(a) has fewer instructions (b) has fewer addressing modes

(c) has more registers

(d) is easier to implement using hard-wired control logic

2.23. A certain processor supports only the immediate and the direct addressing

modes. Which of the following programming language features cannot be

implemented on this processor?

(a) Pointers (b) Arrays

(c) Records

(d) Recursive procedures with local variable

2.24. Consider the following C function definition

int Trial (int a, int b, int c)

if ((a > = b) && (c < b) return b;

else if (a > = b) return Trial (a,c,b);

else return Trial (b,a,c);

The function Trial:

(a) Finds the maximum of a, b, and c (b) Finds the minimum of a, b and c

(c) Finds the middle number of a, b, c (d) None of the above

2.25. Which of the following is/are correct?

(a) An SQL query automatically eliminates duplicates

(b) An SQL query will not work if there are no indexes on the relations

(c) SQL permits attribute names to be repeated in the same relation


SECTION – B

This section consists of TWENTY questions of FIVE marks each. Attempt ANY FIFTEEN

questions. If more number of questions are attempted, score off the answer not to be evaluated, else only the first fifteen unscored answers will be considered.

3. (a) Mr. X claims the following:

If a relation R is both symmetric and transitive, then R is reflexive. For this,

Mr. X offers the following proof:





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“From xRy, using symmetry we get yRx. Now because R is transitive xRy and

yRx together imply xRx.

Therefore, R is reflexive”.

(b) Give an example of a relation R which is symmetric and transitive but not

reflexive.

4. Let G be a finite group and H be a subgroup of G. For a ∈ G, define aH=ah1

h∈H).

(a) Show that |aH| = |H|

(b) Show that for every pair of elements a,b ∈G, either aH = bH or aH and bH

are disjoint.

(c) Use the above to argue that the order of H must divide the order of G.

5. Let G be a connected, undirected graph. A cut in G is a set of edges whose

removal results in G being broken into two or more components, which are not

connected with each other. The size of a cut is called its cardinality. A min-cut of G is a cut in G of minimum cardinality. Consider the following graph.

(a) Which of the following sets of edges is a cut?

(i) (A, B), (E, F), (B, D), (A, E), (A, D)]

(ii) (B, D), (C, F), (A,B)

(b) What is the cardinality of min-cut in this graph?

(c) Prove that if a connected undirected graph G with n vertices has a min-cut of cardinality k, then G has at least (nk/2) edges.

6. (a) Given that A is regular and (A ∪B) is regular, does it follow that B is

necessarily regular ? Justify your answer.

(b) Given two finite automata M1, M2, outline an algorithm to decide if L(M1) ⊆

L(M2). (note: strict subset)

7. Show that the language Lxcx 1 x ∈ 0,1* and c is a terminal symbol is not

context free c is not 0 or 1.

8. Let Abe an n × n matrix such that the elements in each row and each column are

arranged in ascending order. Draw a decision tree, which finds 1st, 2nd and 3rd smallest elements in minimum number of comparisons.

B

A E

F C

D





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9. Let synthesized attribute val give the value of the binary number generated by S

in the following grammar. For example, on input 101, 101, S.val = 5.625.

S LL\L

L LB\B

B 0\1

Write S-attributed values corresponding to each of the productions to find S.val.

10. Suppose we have a function HALTS which when applied to any arbitrary function f

and its arguments will say TRUE if function f terminates for those arguments and

FALSE otherwise. Example: Given the following function definition.

FACTORIAL (N) = IF (N = 0) THEN 1 ELSE N*FACTORIAL (N-1)

Then HALTS (FACTORIAL 4) = TRUE and HALTS (FACTORIAL –5)=FALSE

Let us define the function. FUNNY (f) = IF HALTS (f f) THEN not (f f) ELSE TRUE

(a) Show that FUNNY terminates for all functions f.

(b) use (a) to prove (by contradiction) that it is not possible to have a function

like HALTS which for arbitrary functions and inputs says whether it will terminate on that input or not.

11. (a) Consider the following algorithms. Assume, procedure A and procedure B

take ( ) (1) and ( ) (1/n) unit of time respectively. Derive the time complexity of the algorithm in ( )-notation.

algorithm what (n)

begin

if n = 1 then call A

else begin

what (n –1);

call B(n)

end

end.

(b) Write a constant time algorithm to insert a node with data D just before the

node with address p of a singly linked list.

12. (a) In binary tree, a full node is defined to be a node with 2 children. Use

induction on the height of the binary tree to prove that the number of full

nodes plus one is equal to the number of leaves.

(b) Draw the min-heap that results from insertion of the following elements in

order into an initially empty min-heap: 7, 6, 5, 4, 3, 2, 1. Show the result after the deletion of the root of this heap.





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13. An instruction pipeline consists of 4 stages – Fetch (F), Decode field (D). Execute

(E) and Result Write (W). The 5 instructions in a certain instruction sequence

need these stages for the different number of clock cycles as shown by the table below.

No. of clock cycles needed for

Instruction F D E W

1 1 2 1 1

2 1 2 2 1

3 2 1 3 2

4 1 3 2 1

5 1 2 1 2

Find the number of clock cycles needed to perform the 5 instructions.

14. (a) Show that the formual [(~p∨q) ⇒ (q ⇒ P)] is not a tautology.

(b) Let A be a tautology and B be any other formula. Prove that (A∨B) is a

tautology.

15. What will be the output of the following program assuming that parameter passing is

(i) call by value

(ii) call by reference

(iii) call by copy restore

procedure Px,y,z;

begin y: y + 1; z: x + x end;

begin

a: = : b : =3;

P(a+b,a,a);

Print (a)

end.

16. Consider the following Pascal program skeleton:

program sort (…);

var a,x,….;

procedure readarray;

vari i, …..;

begin

…:=…a…

end;





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procedure exchange (…);

begin

…:=…a…;

…:=…x…;

end;

procedure qsort(….);

var k,v, ….;

function partition (…)…;

var i,j,…;

begin

…:=…a…;

…:=…v…;

end;

begin

:

end:

begin

:

end.

Assume that given points in time during program execution, following procedures

are active: sort, qsort (1,9), qsort (1,3), partition (1,3), exchange (1,3)

Show snapshots of the runtime stack with access links after each of the

activations.

17. Consider the following program fragment in the assembly language of a certain

hypothetical processor. The processor has three general purpose registers R1, R2

and R3. The meanings of the instructions are shown by comments (starting with ;) after the instructions.

X: CMP R1,0 ; Compare R1 and 0, set flags appropriately in status register

JZZ ; Jump if zero to target Z.

MOV R2, R1 ; Copy contents of R1 to R2

SHR R1 ; Shift right R1 by 1 bit

SHL R1 ; Shift left R1 by 1 bit

CMP R2, R1 ; Compare R2 and R1 and set flag in status register

JZY ; Jump if zero to target Y

INC R3 ; Increment R3 by 1;

Y: SHR R1 ; Shift right R1 by 1 bit

JMP X ; Jump to target X

Z:….





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(a) Initially R1, R2 and R3 contain the values 5,0 and 0 respectively, what are the final values of R1 and R3 when control reaches Z?

(b) In general, if R1, R2 and R3 initially contain the values n, 0, and 0

respectively. What is the final value of R3 when control reaches Z?

18. Design a 2K × 8 (2048 locations, each bit wide) memory system mapped at

addresses ( ) ( )16 16

1000 to 17FF for the 8085 processor using four 1K × 4 memory

chips. Each of these chips has the following signal pins:

(i) CS (Chip select, data lines are in high impedance state when it is 1)

(ii) RD (0 for read operation)

(iii) WR (0 for write operation)

(iv) A0, A1, …A9 (input address lines. A0 is the lest significant)

(v) D0, D1, D2, D3 (bi-directional data lines. D0 is the least significant)

19. A certain computer system has the segmented paging architecture for virtual

memory. The memory is byte addressable. Both virtual and physical address

spaces contain 162 bytes each. The virtual address space is divi8ded into 8 non-

overlapping equal size segments. The memory management unit (MMU) has a

hardware segment table, each entry of which contains the physical address of the

page table for the segment. Page table are stored in the main memory and consists of 2 byte page table entries.

(a) What is the minimum page size in bytes so that the page table for a segment

requires at most one page to store it? Assume that the page size can only be a power of 2

(b) Now suppose that the pages size is 512 bytes. It is proposed to provide a

TLB (Translation look-aside buffer) for speeding up address translation. The

proposed TLB will be capable of storing page table entries for 16 recently

referenced virtual pages, in a fast cache that will use the direct mapping

scheme. What is the number o tag bits that will need to be associated with each cache entry

(c) Assume that each page table entry contains (besides other information) 1

valid bit, 3 bits for page protection and 1 dirty bit. How many bits are

available in page table entry for storing the aging information for the page?

Assume that the page size is 512 bytes.

20. (a) A certain processor provides a ‘test and set’ instruction that is used as

follows.

TSET register.flag

This instruction atomically copies flag to register and sets flag to 1. Give

pseudopodia for implementing the entry and exit code to a critical region using this instruction.

(b) Consider the following solution to the producer-consumer problem suing a

buffer of size 1. Assume that the initial value of account is 0. Also assume that the testing of count and assignment to count are atomic operations.





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Producer

Repeat

Produce an item;

if count = 1 then sleep;

place item in buffer.

Count =1:

Wakeup (Consumer);

Forever

Consumer:

Repeat

if count = 0 then sleep;

Remove item from buffer;

Count = 0

Wakeup (producer);

Consumer item;

Forever:

Show that in this solution it is possible that both the processes are sleeping at

the same time.

21. Consider a B-tree with degree m. that is, the number of children, c, of any

internal node (except the root) is such that m ≤ c ≤ 2m –1. derive the maximum

and minimum number of records in the leaf nodes for such a B-tree with height h.h≥1. (Assume that the root of a tree is at height 0).

22. Consider the set of relations

EMP (Employee-no. Dept-no, Employee-name, Salary)

DEPT (Dept-no. Dept-name, Location)

Write an SQL query to:

(a) Find all employee names who work in departments located at ‘Calcutta’ and

whose salary is greater than Rs.50,000.

(b) Calculate, for each department number, the number of employees with a

salary greater than Rs.1,00,000.





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SECTION - A

1. This question consists of TWENTY-THREE multiple questions of ONE mark each.

For each question (1.1 – 1.23), four possible alternatives (A, B, C and D) are

given, out of which ONLY ONE is correct. Indicate the correct answer in the boxes

corresponding to the questions only on the FIRST sheet of the answer book.

1.1 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52

cards to guarantee that three cards are from some same suit is

(a) 3 (b) 8 (c) 9 (d) 12

1.2 An n × n array v is defined as follows:

, for all , , ,1i j i j i j i i n j nν = − ≤ ≤ ≤ ≤

The sum of the elements of the array v is

(a) 0 (b) n -1 (c) 2 3 2n n− + (d) ( )2 1

2

nn

+

1.3 The determinant of the matrix

2 0 0 0

8 1 7 2

2 0 2 0

9 0 6 1

is:

(a) 4 (b) 0 (c) 15 (d) 20

1.4 Let S and T be language over Σ=a,b represented by the regular expressions (a+b*)* and (a+b)*, respectively. Which of the following is true?

(a) S ⊂ T (b) T ⊂ S (c) S = T (d) S ∩T = φ

1.5 Let L denotes the language generated by the grammar S 0S0/00.


(a) L = 0+ (b) L is regular but not 0+

(c) L is context free but not regular (d) L is not context free

1.6 The number 43 in 2’s complement representation is

(a) 01010101 (b) 11010101 (c) 00101011 (d) 10101011

1.7 To put the 8085 microprocessor in the wait state

(a) lower the HOLD input (b) lower the READY input

(c) raise the HOLD input (d) raise the READY input





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1.8 Comparing the time T1 taken for a single instruction on a pipelined CPU with time

T2 taken on a non-pipelined but identical CPU, we can say that

(a) T1 ≤ T2 (b) T1 ≥ T2 (c) T1 < T2

(d) T1 is T2 plus the time taken for one instruction fetch cycle

1.9 The 8085 microprocessor responds to the present of an interrupt

(a) as soon as the TRAP pin becomes ‘high’

(b) by checking the TRAP pin for ‘high’ status at the end of each instruction each

(c) by checking the TRAP pin for ‘high’ status at the end of the execution of each

instruction.

(d) by checking the TRAP pin for ‘high’ status at regular intervals.

1.10 The most appropriate matching for the following pairs

X: Indirect addressing 1: Loops

Y: Immediate addressing 2: Pointers

Z: Auto decrement addressing 3. Constants

is

(a) X – 3 Y – 2 Z - 1 (b) X – 1 Y – 3 Z - 2

(c) X – 2 Y – 3 Z - 1 (d) X – 3 Y – 1 Z - 2

1.11 The following C declarations

struct node

int i:

float j;

;

struct node *s[10];

define s to be

(a) An array, each element of which is a pointer to a structure of type node

(b) A structure of 2 fields, each field being a pointer to an array of 10 elements

(c) A structure of 3 fields: an integer, a float, and an array of 10 elements

(d) An array, each element of which is a structure of type node


X: m=malloc(5); m= NULL; 1: using dangling pointers

Y: free(n); n->value=5; 2: using uninitialized pointers

Z: char *p; *p=’a’; 3. lost memory





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is:

(a) X – 1 Y – 3 Z - 2 (b) X – 2 Y – 1 Z - 3

(c) X – 3 Y – 2 Z - 1 (d) X – 3 Y – 1 Z - 2


X: depth first search 1: heap

Y: breadth-first search 2: queue

Z: sorting 3: stack

is:

(a) X – 1 Y – 2 Z - 3 (b) X – 3 Y – 1 Z - 2

(c) X – 3 Y – 2 Z - 1 (d) X – 2 Y – 3 Z - 1

1.14 Consider the following nested representation of binary trees: (X Y Z) indicates Y

and Z are the left and right sub stress, respectively, of node X. Note that Y and Z

may be NULL, or further nested. Which of the following represents a valid binary tree?

(a) (1 2 (4 5 6 7)) (b) (1 (2 3 4) 5 6) 7)

(c) (1 (2 3 4)(5 6 7)) (d) (1 (2 3 NULL) (4 5))

1.15 Let s be a sorted array of n integers. Let t(n) denote the time taken for the most

efficient algorithm to determined if there are two elements with sum less than 1000 in s. which of the following statements is true?

(a) t (n) is 0(1) (b) n ≤ t(n) ≤ n log2 n

(c) n log2 n ≤ t(n) < 2

n

(d) t(n) = 2

n

1.16 Aliasing in the context of programming languages refers to

(a) multiple variables having the same memory location

(b) multiple variables having the same value

(c) multiple variables having the same identifier

(d) multiple uses of the same variable

1.17 Consider the following C declaration struct

short s [5]

union

float y;

long z;

u;

t;





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Assume that objects of the type short, float and long occupy 2 bytes, 4 bytes and

8 bytes, respectively. The memory requirement for variable t, ignoring alignment

considerations, is

(a) 22 bytes (b) 14 bytes (c) 18 bytes (d) 10 bytes

1.18 The number of tokens in the following C statement

printf(“i=%d, &i=%x”,i,&i);

is

(a) 3 (b) 26 (c) 10 (d) 21

1.19. Which of the following derivations does a top-down parser use while parsing an input string? The input is assumed to be scanned in left to right order.

(a) Leftmost derivation

(b) Leftmost derivation traced out in reverse

(c) Rightmost derivation

(d) Rightmost derivation traced out in reverse

1.20. Which of the following need not necessarily be saved on a context switch

between processes?

(a) General purpose registers (b) Translation look-aside buffer

(c) Program counter (d) All of the above

1.21. Let m[0]…m[4] be mutexes (binary semaphores) and P[0] …. P[4] be processes.

Suppose each process P[i] executes the following:

wait (m[i];wait (m[(i+1) mode 4]);

………

release (m[i]); release (m[(i+1)mod 4]);

This could cause

(a) Thrashing (b) Deadlock

(c) Starvation, but not deadlock (d) None of the above

1.22. B+ -trees are preferred to binary trees in databases because

(a) Disk capacities are greater than memory capacities

(b) Disk access is much slower than memory access

(c) Disk data transfer rates are much less than memory data transfer rates

(d) Disks are more reliable than memory

1.23. Given the relations

employee (name, salary, deptno), and

department (deptno, deptname, address)





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Which of the following queries cannot be expressed using the basic relational

algebra operations (σ,π,×, ,∪,∩,−)?

(a) Department address of every employee

(b) Employees whose name is the same as their department name

(c) The sum of all employees’ salaries

(d) All employees of a given department

2. This question consists of TWENTY-SIX multiple questions of TWO marks each.

For each question (2.1 – 2.26), four possible alternatives (A, B, C and D) are

given, out of which ONLY ONE is correct. Indicate the correct answer in the boxes corresponding to the questions only on the SECOND sheet of the answer book.

2.1 X,Y and Z are closed intervals of unit length on the real line. The overlap of X and

Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which of the following is true?

(a) k must be 1 (b) k must be 0

(c) k can take any value between 0 and 1 (d) None of the above

2.2. E1 and E2 are events in a probability space satisfying the following constraints:

• Pr(E1) = Pr(E2)

• Pr(E1 ∪ E2) = 1

• E1 and E2 are independent

The value of Pr(E1), the probability of the event E1, is

(a) 0 (b) 1

4 (c)

1

2 (d) 1

2.3. Let 100

23

log l

i

S i=

= ∑ and

and T=100

22

logx xdx∫


(a) S > T (b) S = T

(c) S < T and 2S > T (d) 2S ≤ T

2.4. A polynomial p(x) satisfies the following:

p(1) = p(3) = p(5) = 1

p(2) = p(4) = -1

The minimum degree of such a polynomial is

(a) 1 (b) 2 (c) 3 (d) 4





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2.5. A relation R is defined on the set of integers as x Ry iff (x+y) is even. Which of

the following statements is true?

(a) R is not an equivalence relation

(b) R is an equivalence relation having 1 equivalence class

(c) R is an equivalence relation having 2 equivalence classes

(d) R is an equivalence relation having 3 equivalence classes

2.6. Let P(S) denotes the powerset of set S. Which of the following is always true?

(a) P(P(S))=P(S) (b) P(S) ∩P(P(S)) = φ

(c) P(S) ∩S = P(S) (d) S ∉P(S)

2.7. Let a, b, c, d be propositions. Assume that the equivalence a ↔ (b V-b) and b ↔

c hold. Then the truth-value of the formula ( ) ( )a b a c d∧ → ∧ ∨ is always

(a) True (b) False

(c) Same as the truth-value of b (d) Same as the truth-value of d

2.8. What can be said about a regular language L over a whose minimal finite state

automation has two states?

(a) L must be an|n is odd (b) L must be an|n is even

(c) L must be an|≥0

(d) Either L must be an|n is odd, or L must be an| n is even

2.9. Consider the following decision problems:

(P1) Does a given finite state machine accept a given string

(P2) Does a given context free grammar generate an infinite number of stings


(a) Both (P1) and (P2) are decidable

(b) Neither (P1) nor (P2) are decidable

(c) Only (P1) is decidable (d) Only (P2) is decidable

2.10. The simultaneous equations on the Boolean variables x, y, z and w,

1

0

1

w=0

x y z

xy

xz w

xy z

+ + =

=

+ =

+

have the following solution for x, y, z and w, respectively:

(a) 0 1 0 0 (b) 1 1 0 1 (c) 1 0 1 1 (d) 1 0 0 0





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2.11. Which functions does NOT implement the Karnaugh map given below?

wz 00 01 11 10

xy↓

00 0 × 0 0

01 0 × 1 1

11 1 1 1 1

10 0 × 0 0

(a) ( )w x y+ (b) xy yw+

(c) ( ) ( ) ( )w x w y x y+ + + (d) None of the above

2.12. The following arrangement of master-slave flip flops

has the initial state of P, Q as 0, 1 (respectively). After the clock cycles the

output state P, Q is (respectively),

(a) 1, 0 (b) 1, 1 (c) 0, 0 (d) 0, 1

2.13. A graphics card has on board memory of 1 MB. Which of the following modes can

the card not support?

(a) 1600 × 400 resolution with 256 colours on a 17 inch monitor

(b) 1600 × 400 resolution with 16 million colours on a 14 inch monitor

(c) 800 × 400 resolution with 16 million colours on a 17 inch monitor

(d) 800 × 800 resolution with 256 colours on a 14 inch monitor

2.14. Consider the values of A = 2.0 × 1030, B = -2.0 × 1030, C = 1.0, and the sequence

X: = A + B Y:= A + c

X: = X + C Y:= Y + B

Executed on a computer where floating point numbers are represented with 32

bits. The values for X and Y will be

(a) X = 1.0, Y = 1.0 (b) X = 1.0, Y = 0.0

(c) X = 0.0, Y = 1.0 (d) X = 0.0, Y = 0.0

P

J K

Q 1

D

1

Clock





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2.15. Suppose you are given an array s[1…n] and a procedure reverse (s,i,j) which

reverses the order of elements in a between positions i and j (both inclusive).

What does the following sequence do, where 1 ≤ k ≤n:

reverse (s, 1, k);

reverse (s, k + 1, n);

reverse (s, 1, n);

(a) Rotates s left by k positions (b) Leaves s unchanged

(c) Reverses all elements of s (d) None of the above

2.16. Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a

postorder, inorder and preorder traversal. Respectively, of a complete binary tree. Which of the following is always tree?

(a) LASTIN = LASTPOST (b) LASTIN = LASTPRE

(c) LASTPRE = LASTPOST (d) None of the above

2.17. Consider the following functions

( )

( )( )

2log

3

2

!

n

n n

f n n

g n

h n n

=

=

=


(a) h(n) is O (f(n)) (b) h(n) is O (g(n))

(c) g(n) is not O (f(n)) (d) f(n) is O(g(n))

2.18. Let G be an undirected connected graph with distinct edge weight. Let maxe be the

edge with maximum weight and mine the edge with minimum weight. Which of

the following statements is false?

(a) Every minimum spanning tree of G must contain mine

(b) If maxe is in a minimum spanning tree, then its removal must disconnect G

(c) No minimum spanning tree contains maxe

(d) G has a unique minimum spanning tree

2.19. Lt G be an undirected graph. Consider a depth-first traversal of G, and let T be

the resulting depth-first search tree. Let u be a vertex in G and let ν be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true?

(a) u,v must be an edge in G, and u is a descendant of v in T

(b) u,v must be an edge in G, and v is a descendant of u in T

(c) If u,v is not an edge in G then u is a leaf in T

(d) If u,v is not an edge in G then u and v must have the same parent in T





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2.20. The value of j at the end of the execution of the following C program

int incr (int i)

static int count = 0;

count = count + i;

return (count);

main ()

int i,j;

for (i = 0; i <=4; i++)

j = incr(i);

is

(a) 10 (b) 4 (c) 6 (d) 7

2.21. Given the following expression grammar:

E E * F | F + E | F

F F - | id


(a) * has higher precedence than + (b) - has higher precedence than *

(c) + and – have same precedence (d) + has higher precedence than *

2.22. Suppose the time to service a page fault is on the average 10 milliseconds, while

a memory access takes 1 microsecond. Then a 99.99% hit ratio results in

average memory access time of

(a) 1.9999 milliseconds (b) 1 millisecond

(c) 9.999 microseconds (d) 1.9999 microseconds

2.23. Which of the following is NOT a valid deadlock prevention scheme?

(a) Release all resources before requesting a new resource

(b) Number the resources uniquely and never request a lower numbered resource than the last one requested.

(c) Never request a resource after releasing any resource

(d) Request and all required resources be allocated before execution.





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2.24. Given the following relation instance

1 4 2

1 5 3

1 6 3

3 2 2

X Y Z

Which of the following functional dependencies are satisfied by the instance?

(a) XY Z and Z Y (b) YZ X and Y Z

(c) YZ X and X Z (d) XZ Y and Y X

2.25. Given relations r(w,x) and s(y,z), the result of

select distinct w,x

from r, s

is guaranteed to be same as r, provided

(a) r has no duplicates and s is non-empty

(b) r and s have no duplicates

(c) s has no duplicates and r is non-empty

(d) r and s have the same number of tuples

2.26 In SQL, relations can contain null values, and comparisons with null values are

treated as unknown. Suppose all comparisons with a null value are treated as

false. Which of the following pairs is not equivalent?

(a) x = 5 not (not (x = 5)

(b) x = 5 x > 4 and x < 6, where x is an integer

(c) x ≠ 5 not (x = 5)


SECTION – B

This section consists of TWENTY questions of FIVE marks each. Attempt ANY FIFTEEN

questions. If more number of questions are attempted, score off the answer not to be evaluated, else only the first fifteen unscored answers will be considered.

3. Consider the following sequence: s1 : s2 =1 and s1 = 1 + mine 1 2,i is s− − for i >

2. Prove by induction on a n that 2

n

ns

=

.

4. Let S = 0, 1, 2, 3, 4, 5, 6, 7 and ⊗ denote multiplication modulo 8, that is , x

⊗ y = (xy) mod 8

(a) Prove that (0,1, ⊗) is not a group.

(b) Write 3 distinct groups (G, ⊗) where G ⊂ S and G has 2 elements.





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5. A multiset is an unordered collection of elements where elements may repeat any

number of times. The size of a multiset is the number of elements in it counting

repetitions.

(a) What is the number of multisets of size 4 that can be constructed from n

distinct elements so that at least one element occurs exactly twice?

(b) How many multisets can be consctructed from n distinct elements?

6. Let S be a set of n elements 1, 2, …., n and G a graph with 2n vertices, each

vertex corresponding to a distinct subset of S. Two vertices are adjacent iff the

symmetric difference of the corresponding sets has exactly 2 elements. Note: The

symmetric difference of two sets R1 and R2 is defined as 1 2

2 1

R R

R R

∪

(a) Every vertex in G has the same degree. What is the degree of a vertex in G?

(b) How many connected components does G have?

7. (a) Construct as minimal finite state machine that accepts the language, over

0,1, of all strings that contain neither the substring 00 nor the substring 11.

(b) Consider the grammar

S aS Ab

S ε

A bA

A ε

Where S, A are non-terminal symbols with S being the start symbol; a,b are

terminal symbols and ε is the empty string. This grammar generates strings of

the form i ja b for some i, j ≥ 0, where i and j satisfy some condition. What is the

condition on the values of i and j?

8. A pushdown automaton (pda) is given in the following extended notation of finite state diagrams:

The nodes denote the states while the edges denote the moves of the pda. The

edge labels are of the form d, /s s′where d is the input symbol read and ,s s′ are

the stack contents before and after the move. For example the edge labeled 1,

s/1.s denotes the move from state to o oq q in which the input symbol 1 is read

and pushed to the stack.

(a) Introduce two edges with appropriate labels in the above diagram so that the

resulting pda accepts the language

2 0,1 *, denotes revese of x ,R Rx x x x∈ by empty stack.

q0 q1

1.s/1.s 1,1.s/s

2.s/s





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(b) Describe a non-deterministic pda with three states in the above notation that

accept the language 0 1 2n m n m n≤ ≤ by empty stack

9. Design a logic circuit to convert a single digit BCD number to the number modulo

six as follows (Do not detect illegal input):

(a) Write the truth table for all bits. Label the input bits I1, I2, …. With I1 as the

least significant bit. Label the output bits R1, R2, …. With R1 as the least

significant bit. Use 1 to signify truth.

(b) Draw one circuit for each output bit using, altogether, two two-input AND

gates, one two-input gate and two NOT gates.

10. Consider the 8085 instruction IN 09H stored as follows:

Memory Address Machine Code

3050

3051

DA

09

And the following incomplete timing diagram for the instruction:

(a) Write the contents of the boxes, A, B, C and D in hexadecimal in your answer

sheet. Do not draw any pictures.

(b) Write the state of both ALE and RD pins at time units T1, T2, T3 and T4.

(c) How do you generate the signal that tells the peripheral to put the data on

the bus? Answer by completing the following statement in your answer book:

By combining signals …………….

11. Consider the following 8085 program segment, where registers B and C contain

BCD values:

S1: MVI A, 99H

MVI D, 00H

SUB C

ADD B

DAA

S2: JC S3

C 30H 30H A15-A8

T1 T2 T3 T4 T5 T6 T7 T8 T9 TA

A 50H AD7 - AD0 D B

IO/M





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MOV E, A

MVI A, 99H

SUB E

MOV E, A

JZ S4

MVI D, FFH

JMP S4

S3: INC A

DAA

MOV E, A

S4: …………

(a) For the two pairs (B = 44, C = 25) and (B = 33, C = 46) at S1,

(i) Find the values in register A when control reaches S2.

(ii) Find the values in registers D and E when control reaches S4.

(b) What, in general, is the value of D and E as a function of B and C when

control reaches S4.

12. An instruction pipeline has five stages where each stage takes 2 nanoseconds

and all instructions use all five stages. Branch instructions are not overlapped,

i.e., the instruction after the branch is not fetched till the branch instruction is completed. Under ideal conditions.

(a) Calculate the average instruction execution time assuming that 20% of all

instruction executed are branch instructions. Ignore the fact that some branch instructions may be conditional.

(b) If a branch instruction is a conditional branch instruction, the branch need

not be taken. If the branch is not taken, the following instructions can be

overlapped. When 80% of all branch instructions are conditional branch

instructions, and 50% of the conditional branch instructions are such that the

branch is taken, calculate the average instruction execution time.

13. Suppose a stack implementation supports, in addition to PUSH and POP, an

operation REVERSE, which reverses the order of the elements on the stack.

(a) To implement a queue using the above stack implementation, show how to

implement ENQUEUE using a single operation and DEQUEUE using a sequence of 3 operations.

(b) The following postfix expression, containing single digit operands and

arithmetic operators + and *, is evaluated using a stack.

5 2 * 3 4 + 5 2 * * +

Show the contents of the stack.

(i) After evaluating 5 2 * 3 4 +

(ii) After evaluating 5 2 * 3 4 + 5 2

(iii) At the end of evaluation.





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14. Consider the line y = ,nx

mwhere n and m are positive integers.

(a) If mq – np < 0, then is the point (p,q) above the line, below the line, or on

the line?

(b) Complete the following function, that returns true if the line segment with

endpoints (p,q) and (r,s) intersects the line ,n

y xm

= by writing the line

number and the content of each box in your answer book.

1: function clash (m, n, p, q, r, s: integer): Boolean;

2: begin

3: clash = false;

4: if (m*q – n * p) 0 then clash : = true;

5: If (m*s – n * r) 0 then clash : = true;

6: if (m*q – n * p) 0 and (m*s – n * r) 0 then clash : = true;

7: if (m*q – n * p) 0 and (m*s – n * r) 0 then clash : = true;

8: end;

15. Suppose you are given arrays p[1…..N] and q[1…….N] both uninitialized that is,

each location may contain an arbitrary value), and a variable count, initialized to 0. Consider the following procedures set and iset:

set (i)

count = count + 1;

q [count] = i;

p[i] = count;

is_set(i)

if (p[i] ≤ 0 or p[i] > count)

return false;

if (q[p[i]] ≠i)

return false;

return true;

(a) Suppose we make the following sequence of calls:

set (7); set (3); set(9);

After these quence of calls, what is the value of count, and what do q[1],

q[2], q[3], p[7], p[3] and p[9] contain?

(b) Complete the following statement “The first count elements of _______

contain values i such that set ( __________) has been called”.

(c) Show that if set (i) has not been called for some i, then regardless of what

p[i] contains, is_set (i) will return false.





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16. A recursive program to compute Fibonacci numbers is shown below. Assume you

are also given an array f[0…..m] with all elements initialized to 0.

fib(n)

if (n > M) error ();

if ( n==0) return 1;

if (n ==1) return 1;

if ( ) _________________(1)

return ____________(2)

t = fib(n – 1) + fib (n – 2);

__________(3)

return t;

(a) Fill in the boxes with expressions/statements to make fib() store and reuse

computed Fibonacci values. Write the box number and the corresponding

contents in your answer book.

(b) What is the time complexity of the resulting program when computing fib(n)?

17. An array contains four occurrences of 0, five occurrences of 1, and three

occurre3nces of 2 in any order. The array is to be sorted using swap operations (elements that are swapped need to be adjacent).

(a) What is the minimum number of swaps needed to sort such an array in the

worst case?

(b) Give an ordering of elements in the above array so that the minimum

number of swaps needed to sort the array is maximum.

18. Consider the following program is pseudo-Pascal syntax.

program main;

var x: integer;

procedure Q [z:integer);

begin

z: z + x;

writeln(z)

end;

procedure P (y:integer);

var x: integer;

begin

x: y + 2;

Q(x);

writeln(x)

end;

begin





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x:=5;

P(x);

Q(x);

writeln(x)

end.

What is the output of the program, when

(a) The parameter passing mechanism is call-by-value and the scope rule is

static scooping?

(b) The parameter passing mechanism is call-by-reference and the scope rule is

dynamic scooping?

19. Consider the syntax directed translation scheme (SDTS) given in the following.

Assume attribute evaluation with bottom-up parsing, i.e., attributes are evaluated immediately after a reduction.

E E1 * T E.val = E1. val * T. val

E T E. val = T. val

T F – T1 T.val = F. val – T1. val

T F T. val = F. val

F 2 F. val =2

F 4 F. val =4

(a) Using this SDTS, construct a parse tree for the expression

4 – 2 – 4 * 2

and also compute its E.val.

(b) It is required to compute the total number of reductions performed to parse

a given input. Using synthesized attributes only, modify the SDTS given,

without changing the grammar, to find E.red, the number of reductions performed while reducing an input to E.

20. (a) Fill in the boxes below to get a solution for the readers-writers problem,

using a single binary semphore, mutex (initialized to 1) and busy waiting. Write the box numbers (1,2 and 3), and their contents in your answer book.

int R = 0, W = 0;

Reader ( )

L1: wait (mutex);

If (W ==0)

R = R +1;





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_______(1)

else

_______(2)

goto L1;

…./* do the read */

wait (mutex)

R = R – 1;

signal (mutex);

Writer ()

L2: wait(mutex);

If ( ) ____(3)

signal (mutex);

goto L2;

W=1;

signal (mutex);

…./*do the write*/

wait(mutex)

W = 0;

signal (mutex);

(b) Can the above solution lead to starvation of writers?

21. (a) Suppose you are given an empty B+-tree where each node (leaf and

internal) can store up to 5 key values. Suppose values 1,2,….. 10 are inserted, in order, into the tree, Show the tree pictorially

(i) After 6 insertions, and

(ii) After all 10 insertions

Do NOT show intermediate stages.

(b) Suppose instead of splitting a node when it is full, we try to move a value to

the left sibling. If there is no left sibling, or the left sibling is full, we split the

node. Show the tree after values, 1, 2,….., 9 have been inserted. Assume, as in (a) that each node can hold up to 5 keys.

(c) In general, suppose a B+-tree node can hold a maximum of m keys, and you

insert a long sequence of keys in increasing order. Then what approximately

is the average number of keys in each leaf level node.

(i) In the normal case, and

(ii) With the insertion as in (b).





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22. Consider a bank database with only one relation

transaction (transno, acctno, date, amount)

The amount attribute value is positive for deposits and negative for withdrawals.

(a) Define an SQL view TP containing the information.

(acctno, T1.date, T2.amount)

for every pair of transactions T1, T2 such that T1 and T2 are transaction on

the same account and the date of T2 is ≤ the date of T1.

(b) Using only the above view TP, write a query to find for each account the

minimum balance it ever reached (not including the 0 balance when the

account is created). Assume there is at most one transaction per day on each

account, and each account has had atleast one transaction since it was

created. To simply your query, break it up into 2 steps by defining an

intermediate view V.





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SECTION - A

1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark

each. For each of these sub-questions, four possible alternatives, A, B, C and D

are provided. Choose the most appropriate alternative and darken its bubble on

the Objective Response Sheet (ORS) against the corresponding sub-question

number using a soft HB pencil. Do not darken more than one bubble for any

sub-question. Do not use the ORS for any rough work. You may use the answer

book for any rough work, if needed.


S1: The sum of two singular n × n matrices may be non-singular

S2: The sum of two n × n non-singular matrices may be singular.

Which of the following statements is correct?

(a) S1 and S2 are both true (b) S1 is true, S2 is false

(c) S1 is false, S2 is true (d) S1 and S2 are both false

1.2 Consider the following relations:

R1 (a,b) iff (a+b) is even over the set of integers

R2 (a,b) iff (a+b) is odd over the set of integers

R3 (a,b) iff a.b > 0 over the set of non-zero rational numbers

R4 (a,b) iff |a – b| ≤ 2 over the set of natural numbers


(a) R1 and R2 are equivalence relations, R3 and R4 are not

(b) R1 and R3 are equivalence relations, R2 and R4 are not

(c) R1 and R4 are equivalence relations, R2 and R3 are not

(d) R1, R2, R3 and R4 are all equivalence relations

1.3 Consider two well-formed formulas in prepositional logic

F1: P ⇒ ¬P F2: (P⇒¬P)∨(¬P⇒P)


(a) F1 is satisfiable, F2 is valid (b) F1 unsatisfiable, F2 is satisfiable

(c) F1 is unsatisfiable, F2 is valid (d) F1 and F2 are both satisfiable

1.4 consider the following two statements:

S1: 20 1n n ≥ is a regular language

S2: 0 1 0 1 and 1m n m n m n+ ≥ ≥ is a regular language


(a) Only S1 is correct (b) Only S2 is correct

(c) Both S1 and S2 are correct (d) None of S1 and S2 is correct





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1.5 Which of the following statements s true?

(a) If a language is context free it can always be accepted by a deterministic

push-down automaton

(b) The union of two context free languages is context free

(c) The intersection of two context free languages is context free

(d) The complement of a context free language is context free

1.6 Given an arbitary non-deterministic finite automaton (NFA) with N states, the

maximum number of states in an equivalent minimized DFA is at least

(a) N2 (b) 2N (c) 2N (d) N!

1.7 More than one word are put in one cache block to

(a) exploit the temporal locality of reference in a program

(b) exploit the spatial locality of reference in a program

(c) reduce the miss penalty



(a) Virtual memory implements the translation of a program’s address space into

physical memory address space

(b) Virtual memory allows each program to exceed the size of the primary memory

(c) Virtual memory increases the degree of multiprogramming

(d) Virtual memory reduces the context switching overhead

1.9 A low memory can be connected to 8085 by using

(a) INTER (b) RESET IN (c) HOLD (d) READY

1.10 Suppose a processor does not have any stack pointer register. Which of the

following statements is true?

(a) It cannot have subroutine call instruction

(b) It can have subroutine call instruction, but no nested subroutine calls

(c) Nested subroutine calls are possible, but interrupts are not

(d) All sequences of subroutine calls and also interrupts are possible





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yz

wx

1.11 Given the following Karnaugh map, which one of the following represents the

minimal Sum-Of-Products of the map?

(a) xy y z′+ (b) wx y xy xz′ ′ + + (c) w x y z xy′ ′+ + (d) xz+y

1.12 A processor needs software interrupt to

(a) test the interrupt system of the processor

(b) implement co-routines

(c) obtain system services which need execution of privileged instructions

(d) return from subroutine

1.13 A CPU has two modes-privileged and non-privileged. In order to change the mode

from privileged to non-privileged

(a) a hardware interrupt is needed

(b) a software interrupt is needed

(c) a privileged instruction (which does not generate an interrupt) is needed

(d) a non-privileged instruction (which does not generate an interrupt is needed

1.14 Randomized quicksort is an extension of quicksort where the pivot is chosen

randomly. What is the worst case complexity of sorting n numbers using randomized quicksort?

(a) O(n) (b) O(n log n) (c) O(n2) (d) O(n!)

1.15 Consider any array representation of an n element binary heap where the

elements are stored from index 1 to index n of the array. For the element stored

at index i of the array (i≤n), the index of the parent is

(a) i-1 (b) 2

i (c)

2

i (d)

( )12

i +

00 01 11 10

00 0 X 0 X

01 X 1 X 1

11 0 X 1 0

10 0 1 X 0





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1.16 Let ( ) ( ) ( )102 log and logf n n n g n n n= = be two positive functions of n. Which of

the following statements is correct?

(a) f(n) = O(g(n) and g(n) ≠O(f(n)) (b) g(n) = O(f(n) and f(n) ≠O(g(n))

(c) f(n)≠O(g(n)) and g(n) ≠O(f(n)) (d) f(n)=O(g(n)) and g(n) =O(f(n))

1.17 The process of assigning load addresses to the various parts of the program and

adjusting the code and date in the program to reflect the assigned addresses is called

(a) Assembly (b) Parsing

(c) Relocation (d) Symbol resolution


(a) An unambiguous grammar has same leftmost and rightmost derivation

(b) An LL(1) parser is a top-down parser

(c) LALR is more powerful than SLR

(d) An ambiguous grammar can never be LR(k) for any k

1.19 Consider a set of n tasks with known runtimes r1, r2, …. rn to be run on a

uniprocessor machine. Which of the following processor scheduling algorithms will result in the maximum throughput?

(a) Round-Robin (b) Shortest-Job-First

(c) Highest-Response-Ratio-Next (d) First-Come-First-Served

1.20 Where does the swap space reside?

(a) RAM (b) Disk

(c) ROM (d) On-chip cache

1.21 Consider a virtual memory system with FIFO page replacement policy. For an

arbitrary page access pattern, increasing the number of page frames in main memory will

(a) always decrease the number of page faults

(b) always increase the number of page faults

(c) sometimes increase the number of page faults

(d) never affect the number of page faults

1.22 Which of the following requires a device driver?

(a) Register (b) Cache (c) Main memory (d) Disk





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1.23 Consider a schema R(A,B,C,D) and functional dependencies A B and C D.

Then the decomposition of R into R1 (AB) and R2(CD) is

(a) dependency preserving and lossless join

(b) lossless join but not dependency preserving

(c) dependency preserving but not lossless join

(d) not dependency preserving and not lossless join

1.24 Suppose the adjacency relation of vertices in a graph is represented in a table

Adj (X,Y). Which of the following queries cannot be expressed by a relational

algebra expression of constant length?

(a) List of all vertices adjacent to a given vertex

(b) List all vertices which have self loops

(c) List all vertices which belong to cycles of less than three vertices

(d) List all vertices reachable from a given vertex

1.25 Let r and s be two relations over the relation schemes R and S respectively, and

let A be an attribute in R. then the relational algebra expression A aσ = (r s) is

always equal to

(a) A aσ = (r) (b) r

(c) A aσ = (r) s (d) None of the above

2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks

each. For each of these sub-questions, four possible alternatives, A,B, C and D




sub-question. Do not use the ORS for any rough work. You may use the answer book for any rough work, if needed.

2.1 How many 4-digit even numbers have all 4 digits distinct?

(a) 2240 (b) 2296 (c) 2620 (d) 4536


S1: There exists infinite sets A, B, C such that A∩(B∪C) is finite.

S2: There exists two irrational numbers x and y such that (x+y) is rational.

Which of the following is true about S1 and S2?







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2.3 Let f: A B be a function, and let E and F be subsets of A. Consider the following

statements about images.

S1:f(E∪F)=f(E) ∪f(F)

S2:f(E∩F)=f(E) ∩f(F)

Which of the following is true about S1 and S2?



2.4 Seven (distinct) car accidents occurred in a week. What is the probability that

they all occurred on the same day?

(a) 7

1

7 (b)

6

1

7 (c)

7

1

2 (d)

7

7

2

2.5 Consider a DFA over ,a b=∑ accepting all strings which have number of a’s

divisible by 6 and number of b’s divisible by 8. What is the minimum number of states that the DFA will have?

(a) 8 (b) 14 (c) 15 (d) 48

2.6 Consider the following languages:

1 , *L ww w a b= ∈

2 , *, is the reverse of wR RL ww w a b w= ∈

23 0 i is an integeriL =

2

3 0 i is an integeriL =

Which of the languages are regular?

(a) Only L1 and L2 (b) Only L2, L3 and L4

(c) Only L3 and L4 (d) Only L3

2.7 Consider the following problem X.

Given a Turing machine M over the input alphabet Σ, any state q of M

And a word w ∈Σ*, does the computation of M on w visit the state q?

Which of the following statements about X is correct?

(a) X is decidable

(b) X is undecidable but partially decidable

(c) X is undecidable and not even partially decidable

(d) X is not a decision problem





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2.8 Consider the following circuit with initial state Q0 = Q1 = 0. The D Flip-flops are

positive edged triggered and have set up times 20 nanosecond and hold times 0.

Consider the following timing diagrams of X and C; the clock period of C≥40

nanosecond. Which one is the correct plot of Y?

(a)

(b)

(c)

(d)

2.9 Which is the most appropriate match for the items in the first column with the

items in the second column

X. Indirect Addressing I. Array implementation

Y. Indexed Addressing II. Writing re-locatable code

Z. Base Register Addressing III. Passing array as parameter

(a) (X, III) (Y, I) (Z, II) (b) (X, II) (Y, III) (Z, I)

(c) (X, III) (Y, II) (Z, I) (d) (X, I) (Y, III) (Z, II)

Y

C

X D0

Clock Clock

D1 Q1

0Q

C

X





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2.10 The 2’s complement representation of ( )10

539− is hexadecimal is

(a) ABE (b) DBC (c) DE5 (d) 9E7

2.11 Consider the circuit shown below. The output of a 2:1 Mux is given by the

function ( ).ac bc′ +


(a) 1 2f x x′= + (b) 1 2 1 2f x x x x′ ′= +

(c) 1 2 1 2f x x x x′ ′= + (d) 1 2f x x ′= +

2.12 Consider the circuit given below with initial state Q0 =1, Q1 = Q2 = 0. The state of

the circuit is given by the value 2 1 04 2Q Q Q+ +

Which one of the following is the correct state sequence of the circuit?

(a) 1,3,4,6,7,5,2 (b) 1,2,5,3,7,6,4 (c) 1,2,7,3,5,6,4 (d) 1,6,5,7,2,3,4

a

b c

a

b c

MUX MUX

2:1 2:1

g

x1 x2

1

0

f

D0 Q0 D1 Q1 D2 Q2

LSB MSB

Clock





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2.13 Consider the following data path of a simple non-pilelined CPU. The registers A,

B, A1, A2, MDR, the bus and the ALU are 8-bit wide. SP and MAR are 16-bit

registers. The MUX is of size 8 × (2:1) and the DEMUX is of size 8 × (1:2). Each

memory operation takes 2 CPU clock cycles and uses MAR (Memory Address Register) and MDR (Memory Date Register). SP can be decremented locally.

The CPU instruction “push r”, where = A or B, has the specification

M [SP] r

SP SP – 1

How many CPU clock cycles are needed to execute the “push r” instruction?

(a) 2 (b) 3 (c) 4 (d) 5

2.14 Consider an undirected unweighted graph G. Let a breadth-first traversal of G be

done starting from a node r. Let d(r,u) and d(r,v) be the lengths of the shortest

paths from r to u and v respectively in G. If u is visited before v during the

breadth-first traversal, which of the following statements is correct?

(a) d(r,u)<d(r,v) (b) d(r,u)>d(r,v)

(c) d(r,u)≤d(r,v) (d) None of the above

2.15 How many undirected graphs (not necessarily connected) can be constructed out

of a given set 1 2, , nV v v v= K of n vertices?

(a) ( )12

n n − (b) 2n (c) n! (d)

( )122

n n−

2.16 What is the minimum number of stacks of size n required to implement a queue

of size n?

(a) One (b) Two (c) Three (d) Four

A2 A1

B A MUX 1:2

DEMUX 1:2

MAR MDR SP dcr





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2.17 What is printed by the print statements in the program P1 assuming call by

reference parameter passing?

Program P1()

x=10;

y=3;

func1(y,x,x);

print x;

print y;

func1(x,y,z)

y=y+4;

z=x+y+z;

(a) 10, 3 (b) 31, 3

(c) 27, 7 (d) None of the above

2.18 Consider the following three C functions:

[P1] int*g(void)

intx=10;

return(&x);

[P2] int*g(void)

int*px;

*px=10;

return px;

[P3] int*g(void)

int*px

px =(int*)malloc (size of (int));

*px=10;

return px;





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Which of the above three functions are likely to cause problems with pointers?

(a) Only P3 (b) Only P1 and P3

(c) Only P1 and P2 (d) P1, P2 and P3

2.19 Consider the following program

Program P2

var n:int:

procedure W(var x:int)

begin

x=x+1;

printx;

end

procedure D

begin

var n:int;

n=3;

W(n);

End

begin \\begin P2

n = 10;

D;

end

If the language has dynamic scooping and parameters are passed by reference,

what will be printed by the program?

(a) 10 (b) 11 (c) 3


2.20 Which of the following does not interrupt a running process?

(a) A device (b) Timer

(c) Scheduler process (d) Power failure

2.21 Consider a machine with 64 MB physical memory and a 32-bit virtual address space. If the page size is 4KB, what is the approximate size of the page table?

(a) 16 MB (b) 8 MB (c) 2 MB (d) 24 MB





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2.22 Consider Peterson’s algorithm for mutual exclusion between two concurrent

processes i and j. The program executed by process is shown below.

repeat

flag[i]=true;

turn=j;

while (P) do no-op;

Enter critical section, perform actions, then

exit critical section

Flag[i]=false;

Perform other non-critical section actions.

Until false;

For the program to guarantee mutual exclusion, the predicate P in the while loop

should be

(a) flag[j]=true and turn=i (b) flag[j]=true and turn=j

(c) flag[i]=true and turn=j (d) flag[i]=true and turn=i

2.23 R(A,B,C,D) is a relation. Which of the following does not have a lossless join,

dependency preserving BCNF decomposition?

(a) A B, B CD (b) A B, B C, C D

(c) AB C, C AD (d) A BCD

2.24 Which of the following relational calculus expressions is not safe?

(a) ( ) ( ) 1 2t u R t A u A s R t A s A∃ ∈ = ∧ ¬∃ ∈ =

(b) ( )( ) 1 2" "t u R u A x s R t A s A s A u A∀ ∈ = ⇒ ∃ ∈ = ∧ =

(c) ( ) 1t t R¬ ∈

(d) ( ) ( ) 1 2t u R t A u A s R t A s A∃ ∈ = ∧ ∃ ∈ =

2.25 Consider a relation geq which represents “greater than or equal to”, that is,

(x,y)∈ geq only if y≥x.

create table geq

( Ib integer not null

ub integer not null

primary key 1b

foreign key (ub) references geq on delete cascade )

Which of the following is possible if a tuple (x,y) is deleted?

(a) A tuple (z,w) with z > y is deleted

(b) A tuple (z,w) with z > x is deleted





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(c) A tuple (z,w) with w < x is deleted

(d) The deletion of (x,y) is prohibited

SECTION B

This section consists of TWENTY questions of FIVE marks each. Any FIFTEEN out of

these questions have to be answered on the Answer Book provided.

3. (a) prove that powerset ( )A B∩ = powerset(A)∩powerset(B)

(b) Let sum(n)=0+1+2+…..+n for all natural numbers n. give an induction proof

to show that the following equation is true for all natural numbers m and n:

sum(m+n)=sum(m)+sum(n)+mn

4. Consider the function h: N×N N so that h (a,b) = ( )2 1 2 1,ba + − where N

=0,1,2,3,….. is the set of natural numbers.

(a) Prove that the function h is an injection (one-one).

(b) Prove that it is also a Subjection (onto)

5. Construct DFA’s for the following languages:

(a) , *, w has baab as a subsringL w w a b= ∈

(b) , *, w has an odd number of a's and an odd nuber of b'sL w w a b= ∈

6. Give a deterministic PDA for the language 2 1n nL a cb n= ≥ over the alphabet =

, , .a b c=∑ Specify the acceptance state.

7. Let a decision problem X be defined as follows:

X: Given a Turing machine M over Σ and nay word w ∈ Σ,

does M loop forever on w?

You may assume that the halting problem of Turing machine is undecidable but

partially decidable.

(a) Show that X is undecidable.

(b) Show that X is not even partially decidable.





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8. Consider a disk with following specifications: 20 surface, 1000 tracks/surface, 16

sectors/track, data density 1 KB/sector, rotation speed 3000 rpm. The operating

system initiates the transfer between the disk and the memory sector-wise. Once

the head has been placed on the right track, the disk reads a sector in a single

scan. It reads bits from the sector while the head is passing over the sector. The

read bits are formed into bytes in a serial-in-parallel-out buffer and each byte is

then transferred to memory. The disk writing is exactly a complementary process.

For parts (c) and (d) below, assume memory read-write time = 0.1 micro-

second/byte, interrupt driven transfer has an interrupt overhead = 0.4

microseconds, the DMA initialization and termination overhead is negligible compared to the total sector transfer time. DMA requests are always granted.

(a) What is the total capacity of the disk?

(b) What is the data transfer rate?

(c) What is the percentage of time the CPU is required for this disk I/O for byte-wise interrupts driven transfer?

(d) What is the maximum percentage of time the CPU is held up for this disk I/O

for cycle-stealing DMA transfer?

9. A CPU has 32-bit memory address and a 256 KB cache memory. The cache is

organized as a 4-way set associative cache with cache block size of 16 bytes.

(a) What is the number of sets in the cache?

(b) What is the size (in bits) of the tag field per cache block?

(c) What is the number and size of comparators required for tag matching?

(d) How many address bits are required to find the byte offset within a cache

block?

(e) What is the total amount of extra memory (in bytes) required for the tag bits?

10. (a) Is the 3-variable function ( )0,1,2,4f = ∑ its self-dual? Justify your answer.

(b) Give a minimal product-of-sum form of the b output of the following excess-3

to BCD converter.

11. A sequential circuit takes an input stream of 0’s and 1’s and produces an output

stream of 0’s and 1’s. Initially it replicates the input on its output until two

consecutive 0’s are encountered on the input. From then onward, it produces an

output stream, which is the bit-wise complement of input stream until it

encounters two consecutive 1’s, whereupon the process repeats. An example of input and output stream is shown below.

e8 e4 e2 e1

b8

b4

b2

b1

Excess 3 To BCD





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The input stream: 101100 01001011 0 11

The desired output: 101100 10110100 0 11

J-K master-slave flip-flops are to be used to design the circuit.

(a) Give the state transition diagram.

(b) Give the minimized sum-of-product expression for J and K inputs of one of its

state flip-flops.

12. Consider a 5-stage pipeline – IF (Instruction Fetch), ID (Instruction Decode and

register read), EX (Execute), MEM (memory), and WB (Write Back). All (memory

or register) reads take place in the second phase of a clock cycle and writes occur

in the first phase of the clock cycle. Consider the execution of the following instruction sequence:

11: sub r2, r3, r4; /* r2 r3 – r4 */

12: sub r4, r2, r3; /* r4 r2 – r3 */

13: sw r2, 100(r1) /* M[r1+100] r2 */

14: sub r3, r4, r2; /* r3 r4 – r2 */

(a) Show all data dependencies between the four instructions.

(b) Identify the data hazards.

(c) Can all hazards be avoided by forwarding in this case?

13. Consider the following C program:

void abc(char*s)

if(s[0]==’\0’)return;

abc(s+1);

abc(s+1);

printf(“%c”,s[0]);

main()

abc(“123”)

(a) What will be the output of the program?

(b) If abc(s) is called with a null-terminated string s of length n characters (not

counting the null (‘\0’) character), how many characters will be printed by abc(s)?

14. (a) Insert the following keys one by one into a binary search tree in the order

specified.

15, 32, 20, 9, 3, 25, 12, 1

Show the final binary search tree after the insertions.





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(b) Draw the binary search tree after deleting 15 from it.

(c) Complete the statements S1, S2 and S3 in the following function so that the

function computes the depth of a binary rooted at t.

typedef struct tnode

int key;

struct tnode *left, *right;

*Tree;

int depth(Tree t)

int x,y;

it (t ==NULL) return0;

x=depth(t left);

S1: ____________;

S2: if(x>y) return _____________:

S3: else return _____________;

15. Consider a weighted undirected graph with vertex set V = n1,n2,n3,n4,n5,n6

and edge set

E=(n1,n2,2),(n1,n3,8),(n1,n6,3),(n2,n4,4),(n2,n5,12),(n3,n4,7),(n4,n5,9),

(n4,n6,4). The third value in each tuple represents the weight of the edge

specified in the tuple.

(a) List the edges of a minimum spanning tree of the graph.

(b) How many distinct minimum spanning trees does this graph have?

(c) Is the minimum among the edge weights of a minimum spanning tree unique

overall possible minimum spanning trees of a graph?

(d) Is the maximum among the edge weights of a minimum spanning tree unique over all possible minimum spanning trees of a graph?

16. Consider the following grammar with terminal alphabet ,(,), ,*a +∑ and start

symbol E. The production rules of the grammar are:

E aA

E (E)

A +E

A *E

A ε

(a) Compute the FIRST and FOLLOW sets for E and A.

(b) Complete the LL(1) parse table for the grammar.





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17. The syntax of the repeat-until statement is given by the following grammar

S repeat S1 until E

Where E stands for expressions, S and S1 stand for statement. The non-terminals

S and S1 have an attribute code that represents generated code. The non-

terminal E has two attributes. The attribute code represents generated code to

evaluate the expression and store its truth value in a distinct variable, and the

attribute varName contains the name of the variable in which the truth value is

stored? The truth-value stored in the variable is 1 if E is true, 0 if E is false.

Give a syntax-directed definition to generate three-address code for the repeat-

until statement. Assume that you can call a function newlabel( ) that returns a

distinct label for a statement. Use the operator ‘\\’ to concatenate two strings and the function gen(s) to generate a line containing the string s.

18. (a) Remove left-recursion from the following grammar:

S Sa| Sb | a | b

(b) Consider the following grammar:

S aSbS| bSaS |ε

Construct all possible parse trees for the string abab. Is the grammar

ambiguous?

19. Two concurrent processes P1 and P2 want to use two resources R1 and R2 in a

mutually exclusive manner. Initially, R1 and R2 are free. The programs executed

by the two processes are given below.

Program for P1:

S1: While (R1 is busy) do no-op;

S2: Set R1 busy;

S3: While (R2 is busy) do no-op;

S4: Set R2 busy;

S5: Use R1 and R2;

S6: Set R1 free;

S7: Set R2 free;

Program for P2:

Q1: While (R1 is busy) do no-op;

Q2: Set R1 busy;

Q3: While (R1 is busy) do no-op;

Q4: Set R1 busy;

Q5: Use R1 and R2;

Q6: Set R2 free;

Q7: Set R1 free;





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(a) Is mutual exclusion guaranteed for R1 and R2? If not, show a possible

interleaving of the statements of P1 and P2 such that mutual exclusion is

violated (i.e., both P1 and P2 use R1 or R2 at the same time).

(b) Can deadlock occur in the above program? If yes, show a possible

interleaving of the statements of P1 and P2 leading to deadlock.

(c) Exchange the statements Q1 and Q3 and statements Q2 and Q4. Is mutual

exclusion guaranteed now? Can deadlock occur?

20. Consider a disk with the 100 tracks numbered from 0 to 99 rotating at 3000 rpm.

The number of sectors per track is 100. the time to move the head between two successive tracks is 0.2 millisecond.

(a) Consider a set of disk requests to read data from tracks 32, 7, 45, 5 and 10.

Assuming that the elevator algorithm is used to schedule disk requests, and

the head is initially at track 25 moving up (towards larger track numbers),

what is the total seek time for servicing the requests?

(b) Consider an initial set of 100 arbitrary disk requests and assume that no new

disk requests arrive while servicing these requests. If the head is initially at

track 0 and the elevator algorithm is used to schedule disk requests, what is the worst case time to complete all the requests?

21. Consider the relation examinee (regno, name, score), where regno is the primary key to score is a real number.

(a) Write a relational algebra using (∏,σ,ρ,×) to find the list of names which

appear more than once in examinee.

(b) Write an SQL query to list the regno of examinees who have a score greater

than the average score.

(c) Suppose the relation appears (regno, centr_code) specifies the center where

an examinee appears. Write an SQL query to list the centr_code having an examinee of score greater than 80.

22. We wish to construct a B+ tree with fan-out (the number of pointers per node)

equal to 3 for the following set of key values:

80, 50, 10, 70, 30, 100, 90

Assume that the tree is initially empty and the values are added in the order

given.

(a) Show the tree after insertion of 10, after insertion of 30, and after insertion

of 90. Intermediate trees need not be shown.

(b) The key values 30 and 10 are now deleted from the tree in that order. Show

the tree after each deletion.





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SECTION A

1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark






book (last few pages) for any rough work.

1.1 The rank of the matrix1 1

0 0

is

(a) 4 (b) 2 (c) 1 (d) 0

1.2 The trapezoidal rule for integration gives exact result when the integrand is a

polynomial of degree

(a) 0 but not 1 (b) 1 but not 0 (c) 0 or 1 (d) 2

1.3 The solution to the recurrence equation ( ) ( ) ( )12 3 2 1, 1 1k kT T T−= + = is

(a) 2k (b) ( )13 1

2

k + − (c) 2log3

k

(d) 3log2k

1.4 The minimum number of colours required to colour the vertices of a cycle with n nodes in such a way that no two adjacent nodes have the same colour is

(a) 2 (b) 3 (c) 4 (d) 2 22

nn

− +

1.5 In the worst case, the number of comparisons needed to search a singly linked list of length n for a given element is

(a) log n (b) 2

n (c) 2log 1n− (d) n


(a) The set of all rational negative numbers forms a group under multiplication.

(b) The set of all non-singular matrices forms a group under multiplication.

(c) The set of all matrices forms a group under multiplication.

(d) Both B and C are true.

1.7 The language accepted by a Pushdown Automaton in which the stack is limited to

10 items is best described as

(a) Context free (b) Regular

(c) Deterministic Context free (d) Recursive





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1.8 “If X then Y unless Z” is represented by which of the following formulas in

prepositional logic? (“ ¬ “, is negation, “∧” is conjunction, and “” is implication)

(a) (X∧¬Z)Y (b) (X∧Y)¬Z (c) X(Y∧¬Z) (d) (XY)∧¬Z

1.9 A device employing INTR line for device interrupt puts the CALL instruction on the

data bus while

(a) INTA is active (b) HOLD is active

(c) READY is active (d) None of the above

1.10 In 8085 which of the following modifies the program counter?

(a) Only PCHL instruction (b) Only ADD instructions

(c) Only JMP and CALL instructions (d) All instructions

1.11 In serial data transmission, every byte of data is padded with a ‘0’ in the

beginning and one or two ‘1’s at the end of byte because

(a) Receiver is to be synchronized for byte reception

(b) Receiver recovers lost ‘0’s and ‘1’s from these padded bits

(c) Padded bits are useful in parity computation


1.12 Minimum sum of product expression for f(w,x,y,z) shown in Karnaugh-map below

is

(a) xz y z′+ (b) xz zx′ ′+

(c) x y zx′ ′+ (d) None of the above

1.13 Which of the following is not a form of memory?

(a) instruction cache (b) instruction register

(c) instruction opcode (d) translation look-a-side buffer

00 01 11 10

00

01

11

10

wx

yz

0 1 1 0

0 0 1 x

x 0 0 1

x 0 1 1





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1.14 The decimal value 0.25

(a) is equivalent to the binary value 0.1

(b) is equivalent to the binary value 0.01

(c) is equivalent to the binary value 0.00111…

(d) cannot be represented precisely in binary

1.15 The 2’s complement representation of the decimal value –15 is

(a) 1111 (b) 11111 (c) 111111 (d) 10001

1.16 Sign extension is a step in

(a) floating point multiplication

(b) signed 16 bit integer addition

(c) arithmetic left shift

(d) converting a signed integer from one size to another

1.17 In the C language

(a) At most one activation record exists between the current activation record

and the activation record for the main

(b) The number of activation records between the current activation record and

the activation record fro the main depends on the actual function calling sequence.

(c) The visibility of global variables depends on the actual function calling

sequence.

(d) Recursion requires the activation record for the recursive function to be

saved on a different stack before the recursive fraction can be called.

1.18 The results returned by function under value-result and reference parameter

passing conventions

(a) Do not differ

(b) Differ in the presence of loops

(c) Differ in all cases

(d) May differ in the presence of exception

1.19 Relation R with an associated set of functional dependencies, F, is decomposed

into BCNF. The redundancy (arising out of functional dependencies) in the resulting set of relations is

(a) Zero

(b) More than zero but less than that of an equivalent 3NF decomposition

(c) Proportional to the size of F+

(d) Indetermine





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1.20 With regard to the expressive power of the formal relational query languages,

which of the following statements is true?

(a) Relational algebra is more powerful than relational calculus

(b) Relational algebra has the same power as relational calculus.

(c) Relational algebra has the same power as safe relational calculus.


1.21 In 2’s complement addition, overflow

(a) is flagged whenever there is carry from sign bit addition

(b) cannot occur when a positive value is added to a negative value

(c) is flagged when the carries from sign bit and previous bit match


1.22 Which of the following scheduling algorithms is non-preemptive?

(a) Round Robin (b) First-In First-Out

(c) Multilevel Queue Scheduling

(d) Multilevel Queue Scheduling with Feedback

1.23 The optimal page replacement algorithm will select the page that

(a) Has not been used for the longest time in the past.

(b) Will not be used for the longest time in the future.

(c) Has been used least number of times.

(d) Has been used most number of times.

1.24 In the absolute addressing mode

(a) the operand is inside the instruction

(b) the address of the operand is inside the instruction

(c) the register containing the address of the operand is specified inside the

instruction

(d) the location of the operand is implicit

1.25 Maximum number of edges in a n-node undirected graph without self loops is

(a) n2 (b) ( )12

n n − (c) n - 1 (d)

( ) ( )1

2

n n+

2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks






book (last few pages) for any rough work.





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2.1 Consider the following logic circuit whose inputs are functions f1, f2, f3 and output

is f.

Given that

( ) ( )

( ) ( )

( ) ( )

1

2

, , 0,1,3,5 ,

, , 6,7 , and

, , 1,4,5 ,

f x y z

f x y z

f x y z

=

=

=

∑∑∑

f3 is

(a) ( )1,4,5∑ (b) ( )6,7∑

(c) ( )0,1,3,5∑ (d) None of the above

2.2 Consider the following multiplexor where 10, 11, 12, 13 are four data input lines

selected by two address line combinations A1A0 =00,01,10,11 respectively and f is the output of the multiplexor. EN is the Enable input.

The function f(x,y,z) implemented by the above circuit is

(a) xyz ′ (b) xy+z

(c) x+y (d) None of the above

2.3 Let f(A,B) = .A B′ + Simplified expression for function ( )( ), ,f f x y y z+ is

(a) x z′ +

(b) xyz

(c) xy z′ +


f(x,y,z)

f1(x,y,z)

f2(x,y,z)

f3(x,y,z)=?

10 11 12 13 A1

A0 EN

f(x,y,z)=?

4 TO 1 multiplexor

OUTPUT





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2.4 What are the states of the Auxillary Carry (AC) and Carry Flag (CY) after

executing the following 8085 program?

MVI H, 5DH

MIV L, 6BH

MOV A, H

ADD L

(a) AC = 0 and CY =0 (b) AC = 1 and CY =1

(c) AC = 1 and CY =0 (d) AC = 0 and CY =1

2.5 The finite state machine described by the following state diagram with A as

starting state, where an arc label is x

yand x stands for 1-bit input and y stands

for 2-bit output

(a) Outputs the sum of the present and the previous bits of the input.

(b) Outputs 01 whenever the input sequence contains 11

(c) Outputs 00 whenever the input sequence contains 10


2.6 The performance of a pipelined processor suffers if

(a) the pipeline stages have different delays

(b) consecutive instructions are dependent on each other

(c) the pipeline stages share hardware resources

(d) All of the above

2.7 Horizontal microprogramming

(a) does not require use of signal decoders

(b) results in larger sized microinstructions than vertical microprogramming

(c) uses one bit for each control signal

(d) all of the above

2.8 Consider the following declaration of a two-dimensional array in C:

char a[100][100];

Assuming that the main memory is byte-addressable and that the array is stored

starting from memory address 0, the address of a [40][50] is

(a) 4040 (b) 4050 (c) 5040 (d) 5050

0/01

0/00

1/01 1/10

0/01

1/10

A B C





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2.9 The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or

3 children is:

(a) 2

n (b)

( )13

n − (c)

( )12

n − (d)

( )2 1

3

n +

2.10 Consider the following algorithm for searching for a given number x in an

unsorted array A[l..n] having n distinct values:

1. Choose an i uniformly at random from l..nl

2. If A[i]=x then Stop else Goto 1;

Assuming that x is present A, what is the expected number of comparisons made

by the algorithm before it terminates?

(a) n (b) n - 1 (c) 2n (d) 2

n

2.11 The running time of the following algorithm

Procedure A(n)

If n<=2 return(1) else return (A( n ));

Is best described by

(a) O(n) (b) O(log n) (c) O(log log n) (d) O(1)

2.12 A weight-balanced tree is a binary tree in which for each node, the number of

nodes in the let sub tree is at least half and at most twice the number of nodes in

the right sub tree. The maximum possible height (number of nodes on the path

from the root to the furthest leaf) of such a tree on n nodes is best described by

which of the following?

(a) log2n (b) 4

3

log n (c) log3n (d) 3

2

log n

2.13 The smallest finite automaton which accepts the language

length of x is divisible by 3x has

(a) 2 states (b) 3 states (c) 4 states (d) 5 states


(a) The complement of a recursive language is recursive.

(b) The complement of a recursively enumerable language is recursively

enumerable.

(c) The complement of a recursive language is either recursive or recursively

enumerable.

(d) The complement of a context-free language is context-free





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2.15 The Newton-Raphson iteration ( )1

3

2 2n

nn

XX

X+

= +

can be used to solve the

equation

(a) 2 3X = (b) 3 3X = (c) 2 2X = (d) 3 2X =

2.16 Four fair coins are tossed simultaneously. The probability that at least one head

and one tail turn up is

(a) 1

16 (b)

1

8 (c)

7

8 (d)

15

16

2.17 The binary relation S = φ (empty set) on set A = 1,2,3 is

(a) Neither reflexive nor symmetric (b) Symmetric and reflexive

(c) Transitive and reflexive (d) Transitive and symmetric

2.18 The C language is:

(a) A context free language (b) A context sensitive language

(c) A regular language

(d) Parsable fully only by a Turing machine

2.19 To evaluate an expression without any embedded function calls

(a) One stack is enough

(b) Two stacks are needed

(c) As many stacks as the height of the expression tree are needed

(d) A Turning machine is needed in the general case

2.20 Dynamic linking can cause security concerns because

(a) Security is dynamic

(b) The path for searching dynamic libraries is not known till runtime

(c) Linking is insecure

(d) Cryptographic procedures are not available for dynamic linking

2.21 Which combination of the following features will suffice to characterize an OS as a

multi-programmed OS? (A) More than one program may be loaded into main

memory at the same time for execution. (B) If a program waits for certain events

such as I/O, another program is immediately scheduled for execution. (C) If the

execution of a program terminates, another program is immediately scheduled for execution.

(a) A (b) A and B (c) A and C (d) A, B and C





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2.22 In the index allocation scheme of blocks to a file, the maximum possible size of

the file depends on

(a) the size of the blocks, and the size of the address of the blocks.

(b) the number of blocks used for the index, and the size of the blocks.

(c) the size of the blocks, the number of blocks used for the index, and the size

of the address of the blocks.


2.23 A B+ - tree index is to be built on the Name attribute of the relation STUDENT.

Assume that all student names are of length 8 bytes, disk blocks are of size 512

bytes, and index pointers are of size 4 bytes. Given this scenario, what would be

the best choice of the degree (i.e. the number of pointers per node) of the B+ -tree?

(a) 16 (b) 42 (c) 43 (d) 44

2.24 Relation R is decomposed using a set of functional dependencies, F, and relation

S is decomposed using another set of functional dependencies, G. One

decomposition is definitely BCNF, the other is definitely. 3NF, but it is not known

which is which. To make a guaranteed identification, which one of the following

tests should be used on the decompositions? (Assume that the closures of F and G are available).

(a) Dependency-preservation (b) Lossless-join

(c) BCNF definition (d) 3NF definition

2.25 From the following instance of a relation schema R(A,B,C), we can conclude that:

(a) A functionally determines B and B functionally determines C

(b) A functionally determines B and B does not functionally determines C

(c) B does not functionally determines C

(d) A does not functionally determines B and B does not functionally determines

C

A B C

1 1 1

1 1 0

2 3 2

2 3 2





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SECTION B

This section consists of TWENTY questions of FIVE marks each. Any FIFTEEN out of

these questions have to be answered on the Answer Book provided.

3. Let A be a set of n(>0) elements. Let Nr be the number of binary relations on A

and let Nf be the number of functions from A to A.

(a) Give the expression for Nr in terms of n.

(b) Give the expression for Nf in terms of n.

(c) Which is larger for all possible n, Nr or Nf?

4. (a) S = 1,2 , 2,1 is binary relation on set A = 1,2,3. Is it irreflexive? Add

the minimum number of ordered pairs to S to make it an equivalence

relation. Give the modified S.

(b) Let S = a,b and let (S) be the powerset of S. Consider the binary

relation ‘⊆ (set inclusion)’ on (S). Draw the Hasse diagram corresponding

to the lattice ((S),⊆)

5. (a) Obtain the eigen values of the matrix

1 2 34 49

0 2 43 94

0 0 2 104

0 0 0 1

A

= −

−

(b) Determine whether each of the following is a tautology, a contradiction, or

neither (“∨” is disjunction, “∧” is conjunction, “→” is implication, “¬” in

negation, and “↔” is biconditional (if and only if).

(i) ( )A A A↔ ∨

(ii) ( )A B B∨ →

(iii) A ∧ (¬ ( )A B∨

6. Draw all binary trees having exactly three nodes labeled A, B and C on which

Preorder traversal gives the sequence C,B,A.

7. (a) Express the function ( ), ,f x y z xy yz′ ′= + with only one complement operation

and one or more AND/OR operations. Draw the logic circuit implementing the

expression obtained, using a single NOT gate and one or more AND/OR gates.





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(b) Transform the following logic circuit (without expressing its switching

function) into an equivalent logic circuit that employs only 6 NAND gates

each with 2-inputs.

8. Consider the following circuit. A = a2a1a0 and B = b2b1b0 are three bit binary

numbers input to the circuit. The output is Z = z3z2z1z0. R0, R1 and R2 are

registers with loading clock shown. The registers are loaded with their input data

with the falling edge of a clock pulse (signal CLOCK shown) and appears as

shown. The bits of input number A, B and the full adders are as shown in the

circuit. Assume Clock period is greater than the settling time of all circuits.

(a) For 8 clocks pulses on the CLOCK terminal and the inputs A, B as shown,

obtain the output Z (sequence of 4-bit values of Z). Assume initial contents of R0, R1 and R2 as all zeros.

A= 110 011 111 101 000 000 000 000

B= 101 101 011 110 000 000 000 000

Clock No 1 2 3 4 5 6 7 8

(b) What does the circuit implement?

A

EA

CLOCK

b2 a2 a1 b1 b0 a0

b2 a2 a1 b1

b2 a2

EA

EA

Z=z3 z2

z1 z0

REG R0 (6 – bit)

REG R1 (6 – bit)

REG R2 (5 – bit)

B

0





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9. Consider the following 32-bit floating-point representation scheme as shown in

the formal below. A value is specified by 3 fields, a one bit sign field (with 0 for

positive and 1 for negative values), a 24 bit fraction field (with the binary point

being at the left end of the fraction bits), and a 7 bit exponent field (in excess-64

signed integer representation, with 16 being the base of exponentiation). The sign bit is the most significant bit.

(a) It is required to represent the decimal value –7.5 as a normalized floating

point number in the given format. Derive the values of the various fields.

Express your final answer in the hexadecimal.

(b) What is the largest values that can be represented using this format? Express your answer as the nearest power of 10.

10. In a C program, an array is declared as float A[2048]. Each array element is 4

Bytes in size, and the starting address of the array is 0×00000000. This program

is run on a computer that has a direct mapped data cache of size 8 Kbytes, with block (line) size of 16 Bytes.

(a) Which elements of the array conflict with element A[0] in the data cache?

Justify your answer briefly.

(b) If the program accesses the elements of this array one by one in reverse

order i.e., starting with the last element and ending with the first element,

how many data cache misses would occur? Justify your answer briefly.

Assume that the data cache is initially empty and that no other data or instruction accesses are to be considered.

11. The following recursive function in C is a solution to the Towers of Hanoi problem.

Void move (int n, char A, char B, char C)

if (………………………………….)

move (………………………………….);

printf(“Move disk %d from pole %c to pole %c\n”, n, A,C);

move (………………………………….);

Fill in the dotted parts of the solution.

1 24 ?

sign fraction exponent





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12. Fill in the blanks in the following template of an algorithm to compute all pairs

shortest path lengths in a directed graph G with n*n adjacency matrix A.

A[i,j]equals if there is an edge in G from i to j, and 0 otherwise. Your aim in filling in the blanks is to ensure that the algorithm is correct.

INITIALIZATION: For i = 1 … n

For j = 1 … n

if A[i,j]=0 then P[i,j] = _______ else P[i,j] =____;

ALGORITHM: For i = 1 …n

For j = 1 …n

For k = 1 …n

P[__,___]=min_______,_______;

(a) Copy the complete line containing the blanks in the Initialization step and fill

in the blanks.

(b) Copy the complete line containing the blanks in the Algorithm step and fill in

the blanks.

(c) Fill in the blank: The running time of the Algorithm is O(____).

13. (a) In how many ways can a given positive integer n ≥ 2 be expressed as the

sum of 2 positive integers (which are not necessarily distinct). For example,

for n = 3, the number of ways is 2, i.e., 1+2, 2+1. Give only the answer

without any explanation.

(b) In how many ways can a given positive integer n ≥ 3 be expressed as the

sum of 3 positive integers (which are not necessarily distinct). For example,

for n = 4, the number of ways is 3, i.e., 1+2+1, 2+1+1. Give only the answer without any explanation.

(c) In how many ways can a given positive integer n ≥ k be expressed as the

sum of k positive integers (which are not necessarily distinct)? Give only the answer without explanation.

14. The aim of the following question is to prove that the language M | M is the

code of a Turing Machine which, irrespective of the input, halts and outputs a 1,

is undecidable. This is to be done by reducing form the language

, halts on ,M x M x′ ′ which is known to be undecidable. In parts (a) and (b)

describe the 2 main steps in the construction of M. in part (c) describe the key

propery which relates the behaviour of M on its input w to the behaviour of M′on x.

(a) On input w, what is the first step that M must make?

(b) On input w, based on the outcome of the first step, what is the second step

that M must make?

(c) What key property relates the behaviour of M on w to the behaviour of M′on

x?





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15. A university placement center maintains a relational database of companies that

interview students on campus and make job offers to those successful in the

interview. The schema of the database is given below:

COMPANY (cname, clocation) STUDENT (scrollno, sname, sdegree)

INTERVIEW (cname, srollno, idate) OFFER (cname,srollno, osalary)

The COMPANY relation gives the name and location of the company. The

STUDENT relation gives the student’s roll number, name and the degree program

for which the student is registered in the university. The INTERVIEW relation

gives the date on which a students is interviewed by a company. The OFFER

relation gives the salary offered to a student who is successful in a company’s

interview. The key for each relation is indicated by the underlined attributes.

(a) Write relational algebra expressions (using only the operator ,σ,π,∪,− )

for the following queries:

(i) List the rollnumbers and names of those students who attended at least one

interview but did not receive any job offer.

(ii) List the rollnumbers and names of students who went for interviews and

received job offers from every company with which they interviewed.

(b) Write an SQL query to list, for each degree program in which more than five

students were offered jobs, the name of the degree and the average offered salary of students in this degree program.

16. For relation R = (L, M, N , O, P), the following dependencies hold:

M O NO P P L and L MN

R is decomposed into R1 =(L, M, N , P) and R2 = (M, O).

(a) Is the above decomposition a lossless-join decomposition? Explain.

(b) Is the above decomposition dependency-preserving? If not, list all the dependencies that are not preserved.

(c) What is the highest normal form satisfied by the above decomposition?

17. (a) The following table refers to search times for a key in B-trees and B+-trees.

A successful search means that the key exists in the database and

unsuccessful means that it is not present in the database. Each of the entries

X1, X2, X3 and X4 can have a value of either Constant or Variable. Constant

means that the search time is the same, independent of the specific key

value, where Variable means that it is dependent on the specific key value chosen for the search.

Give the correct values for the entries X1, X2, X3 and X4 (for example X1 =

Constant, X2= Constant, X3 = Constant, X4= Constant).

B-tree B+-tree

Successful Search Unsuccessful search Successful Search Unsuccessful search

X1 X2 X3 X4





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(b) Relation R(A,B) has the following view defined on it:

CREATE VIEW V AS

(SELECT R1.A,R2.B

FROM R AS R1, R AS R2

WHERE R1.B=R2.A)

(i) The current contents of relation R are shown below. What are the contents of

the view V?

(ii) The tuples (2,11) and (11,6) are now inserted into R. What are the additional

tupels that are inserted in V?

18. (a) Draw the process state transition diagram of an OS in which (i) each process

is in one of the five states: created, ready, running, blocked (i.e. sleep or

wait), or terminated, and (ii) only non-preemptive scheduling is used by the OS. Label the transitions appropriately.

(b) The functionality of atomic TEST-AND-SET assembly language instruction is

given by the following C function.

int TEST-AND-SET (int *x)

int y;

A1:y=*x;

A2:*x=1;

A3:return y;

(i) Complete the following C functions for implementing code for entering and

leaving critical sections based on the above TEST-AND-SET instruction.

int mutex=0;

void enter-cs()

while (…………………………………);

A B

1 2

2 3

2 4

4 5

6 7

6 8

9 10





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void leave-cs()

…………………………………..;

(ii) Is the above solution to the critical section problem deadlock free and starvation-free?

(iii) For the above solution, show by an example that mutual exclusion is not

ensured if TEST-AND-SET instruction is not atomic.

19. A computer system uses 32-bit virtual address, and 32-bit physical address. The

physical memory is byte addressable, and the page size is 4 kbytes. It is decided

to use two level page tables to translate from virtual address to physical address.

Equal number of bits should be used for indexing first level and second level page

table, and the size of each page table entry is 4 bytes.

(a) Give a diagram showing how a virtual address would be translated to a physical address.

(b) What is the number of page table entries that can be contained in each

page?

(c) How many bits are available for storing protection and other information in each page table entry?

20. The following solution to the single producer single consumer problem uses

semaphores for synchronization.

#define BUFFSIZE 100

buffer buf[BUFFSIZE];

int first=last=0;

semaphore b_full=0;

semaphore b_empty=BUFFSIZE;

void producer()

while (1)

produce an item;

p1: …………………..;

put the item into buff (first);

first=(first+1)%BUFFSIZE;

p2: …………………..;

void consumer()





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while (1)

c1:……………………..

take the item from buf[last];

last=(last+1)%BUFFSIZE;

c2: ……………………..;

consume the item;

(a) Complete the dotted part of the above solution.

(b) Using another semaphore variable, insert one line statement each

immediately after p1, immediately before p2, immediately after c1, and

immediately before c2 so that the program works correctly for multiple procedures and consumers.

21. We require a four state automaton to recognize the regular expression

( ) * .a b abb

(a) Give an NFA for this purpose.

(b) Give a DFA for this purpose.

22. (a) Construct all the parse trees corresponding to i + j * k for the grammar

E E+E

E E*E

E id

(b) In this grammar, what is the precedence of the two operators * and +?

(c) If only one parse tree is desired for any string in the same language, what

changes are to be made so that the resulting LALR(1) grammar is non-ambiguous?





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Q.1 — Q.30 carry one mark each.

1. Consider the following C function.

float f,(float x, int y)

float p, s; int i;

for (s=1,p=1,i=1; i<y; i++)

p *= x/i;

s+=p;

return s;

For large values of y, the return value of the function f best approximates

(A) yX (B) ex (C) ln(1+x) (D) xX

2. Assume the following C variable declaration

int * A[10], B[10][10];

Of the following expressions

I. A[2] II. A[2][3] III. B[1] IV. B[2][3]

which will not give compile-time errors if used as left hand sides of assignment statements in a C program?

(A) I,II, and IV only (B) II, III, and IV only

(C) II and IV only (D) IV only

3. Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) =1

2, the

values of P(A|B) and P(B|A) respectively are

(A) 1

4,1

2 (B)

1

2, 1

4 (C)

1

2, 1 (D) 1,

1

2

4. Let A be a sequence of 8 distinct integers sorted in ascending order. How many

distinct pairs of sequences, B and C are there such that (i) each is sorted in

ascending order, (ii) B has 5 and C has 3 elements, and (iii) the result of merging B and C gives A?

(A) 2 (B) 30 (C) 56 (D) 256

5. n couples are invited to a party with the condition that every husband should be

accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is

(A) 2

*2nn

n

(B) 3n (C) ( )2 !

2n

n (D)

2n

n





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6. Let T(n) be the number of different binary search trees on n distinct elements.

Then T(n)= ( ) ( )1

1 ,n

k

T k T x=

−∑ where x is

(A) n – k + 1 (B) n – k (C) n – k – 1 (D) n – k – 2

7. Consider the set Σ* of all strings over the alphabet Σ = 0, 1. Σ* with the

concatenation operator for strings

(A) does not form a group

(B) forms a non-commutative group

(C) does not have a right identity element

(D) forms a group if the empty string is removed from Σ*

8. Let G be an arbitrary graph with n nodes and k components. If a vertex is

removed from G, the number of components in the resultant graph must necessarily lie between

(A) k and n (B) k – 1 and k + 1

(C) k – 1 and n – 1 (D) k + 1 and n – k

9. Assuming all numbers are in 2’s complement representation, which of the following numbers is divisible by 11111011?

(A) 11100111 (B) 11100100 (C) 11010111 (D) 11011011

10. For a pipelined CPU with a single ALU, consider the following situations

I. The j + 1-st instruction uses the result of the j-th instruction as an operand

II. The execution of a conditional jump instruction

III. The j-th and j + 1-st instructions require the ALU at the same time

Which of the above can cause a hazard?

(A) I and II only (B) II and III only (C) III only (D) All the three

11. Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is

(A) Θ (1) (B) Θ (log n) (C) Θ (n) (D) Θ (n2)

12. Ram and Shyam have been asked to show that a certain problem Π is NP-

complete. Ram shows a polynomial time reduction from the 3-SAT problem to Π,

and Shyam shows a polynomial time reduction from Π to 3-SAT. Which of the following can be inferred from these reductions?

(A) Π is NP-hard but not NP-complete (B) Π is in NP, but is not NP-complete

(C) Π is NP-complete (D) Π is neither NP-hard, nor in NP





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13. Nobody knows yet if P = NP. Consider the language L defined as follows.

( )0 1 * if

otherwise

P NPL

φ

+ ==


(A) L is recursive

(B) L is recursively enumerable but not recursive

(C) L is not recursively enumerable

(D) Whether L is recursive or not will be known after we find out if P = NP

14. The regular expression 0*(10*)* denotes the same set as

(A) (1*0)*1* (B) 0+(0+10)*

(C) (0+1)*10(0+1)* (D) None of the above

15. If the strings of a language L can be effectively enumerated in lexicographic (i.e., alphabetic) order, which of the following statements is true?

(A) L is necessarily finite

(B) L is regular but not necessarily finite

(C) L is context free but not necessarily regular

(D) L is recursive but not necessarily context free

16. Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar?

(A) Removing left recursion alone

(B) Factoring the grammar alone

(C) Removing left recursion and factoring the grammar

(D) None of the above

17. Assume that the SLR parser for a grammar G has n1 states and the LALR parser for G has n2 states. The relationship between n1 and n2 is

(A) n1 is necessarily less than n2 (B) n1 is necessarily equal to n2

(C) n1 is necessarily greater than n2 (D) None of the above

18. In a bottom-up evaluation of a syntax directed definition, inherited attributes can

(A) always be evaluated

(B) be evaluated only if the definition is L-attributed

(C) be evaluated only if the definition has synthesized attributes

(D) never be evaluated





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19. Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an

initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree?

(A) 7 5 1 0 3 2 4 6 8 9 (B) 0 2 4 3 1 6 5 9 8 7

(C) 0 1 2 3 4 5 6 7 8 9 (D) 9 8 6 4 2 3 0 1 5 7

20. Consider the following three claims

I. (n + k)m = Θ(nm) where k and m are constants

II. 2n+1 = O(2n)

III. 22n+1 = O(2n)

Which of these claims are correct?

(A) I and II (B) I and III (C) II and III (D) I, II, and III

21. Consider the following graph

Among the following sequences

I a b e g h f II a b f e h g III a b f h g e IV a f g h b e

Which are depth first traversals of the above graph?

(A) I, II and IV only (B) I and IV only

(C) II, III and IV only (D) I, III and IV only

22. The usual Θ(n2) implementation of Insertion Sort to sort an array uses linear

search to identify the position where an element is to be inserted into the already sorted part of the array. If, instead, we use binary search to identify the position, the worst case running time will

(A) remain Θ(n2) (B) become Θ(n (log n)2)

(C) become Θ(n log n) (D) become Θ(n)





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23. In a heap with n elements with the smallest element at the root, the 7th smallest element can be found in time

(A) Θ(n log n) (B) Θ(n) (C) Θ(log n) (D) Θ(1)

24. Which of the following statements is FALSE?

(A) In statically typed languages, each variable in a program has a fixed type

(B) In un-typed languages, values do not have any types

(C) In dynamically typed languages, variables have no types

(D) In all statically typed languages, each variable in a program is associated with values of only a single type during the execution of the program

25. Using a larger block size in a fixed block size file system leads to

(A) better disk throughput but poorer disk space utilization

(B) better disk throughput and better disk space utilization

(C) poorer disk throughput but better disk space utilization

(D) poorer disk throughput and poorer disk space utilization

26. In a system with 32 bit virtual addresses and 1KB page size, use of one-level page tables for virtual to physical address translation is not practical because of

(A) the large amount of internal fragmentation

(B) the large amount of external fragmentation

(C) the large memory overhead in maintaining page tables

(D) the large computation overhead in the translation process

27. Which of the following assertions is FALSE about the Internet Protocol (IP)?

(A) It is possible for a computer to have multiple IP addresses

(B) IP packets from the same source to the same destination can take different routes in the network

(C) IP ensures that a packet is discarded if it is unable to reach its destination within a given number of hops

(D) The packet source cannot set the route of an outgoing packets; the route is determined only by the routing tables in the routers on the way

28. Which of the following functionalities must be implemented by a transport protocol over and above the network protocol?

(A) Recovery from packet losses (B) Detection of duplicate packets

(C) Packet delivery in the correct order (D) End to end connectivity





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29. Which of the following scenarios may lead to an irrecoverable error in a database system?

(A) A transaction writes a data item after it is read by an uncommitted transaction

(B) A transaction reads a data item after it is read by an uncommitted transaction

(C) A transaction reads a data item after it is written by a committed transaction

(D) A transaction reads a data item after it is written by an uncommitted transaction

30. Consider the following SQL query

select distinct a1, a2, ..., an

from r1, r2, ..., rm

where P

For an arbitrary predicate P, this query is equivalent to which of the following relational algebra expressions?

(A) ( )1 2

1 2, , n

ma a a

r r rρσΠ × × ×K

K

(B) 1 2, , na a a

ρσΠK

(r1 r2 … rm)

(C) ( )1 2

1 2, , n

ma a a

r r rρσΠ ∪ ∪ ∪K

K

(D) ( )1 2

1 2, , n

ma a a

r r rρσΠ ∩ ∩ ∩K

K

Q. 31-90 carry two marks each.

31. Let (S, ≤) be a partial order with two minimal elements a and b, and a maximum

element c. Let P: S True, False be a predicate defined on S. Suppose that

P(a) = True, P(b) = False and P(x) ⇒ P(y) for all x, y ∈ S satisfying x≤y,

where ⇒ stands for logical implication. Which of the following statements CANNOT be true?

(A) P(x) = True for all x ∈ S such that x ≠ b

(B) P(x) = False for all x ∈ S such that x ≠ a and x ≠ c

(C) P(x) = False for all x ∈ S such that b ≤ x and x ≠ c

(D) P(x) = False for all x ∈ S such that a ≤ x and b ≤ x

32. Which of the following is a valid first order formula? (Here α and β are first order formulae with x as their only free variable)

(A) ((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α⇒β]

(B) (∀x)[α] ⇒ (∃x)[α ∧ β]

(C) ((∀x)[α ∨ β] ⇒ (∃x)[α] ⇒ (∀x)[α]

(D) (∀x)[α ⇒ β] ⇒ ((∀x)[α] ⇒ (∀x)[β])





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33. Consider the following formula _ and its two interpretations I1 and I2

α: (∀x)[Px ⇔ (∀y)[Qxy ⇔ ¬Qyy]] ⇒ (∀x)[¬Px]

I1: Domain: the set of natural numbers

Px ≡ ‘x is a prime number’

Qxy ≡ ‘y divides x’

I2: same as I1 except that Px = ‘x is a composite number’.


(A) I1 satisfies α, I2 does not (B) I2 satisfies α, I1 does not

(C) Neither I2 nor I1 satisfies α (D) Both I1 and 12 satisfy α

34. m identical balls are to be placed in n distinct bags. You are given that m ≥ kn,

where k is a natural number ≥1. In how many ways can the balls be placed in the bags if each bag must contain at least k balls?

(A) 1

m k

n

−

− (B)

1

1

m kn n

n

− + −

−

(C) 1m

n k

−

− (D)

2m kn n k

n k

− + + −

−

35. Consider the following recurrence relation

T(1) = 1

T(n + 1) = T(n)+ 1n + for all n≥1

The value of T(m2) for m ≥1 is

(A) 6

m(21m-39)+4 (B)

6

m(4m2-3m+5)

(C) 2

m(3m2.5 -11m+20)-5 (D)

6

m(5m3 -34m2 +137m-104)+

5

6

36. How many perfect matching are there in a complete graph of 6 vertices?

(A) 15 (B) 24 (C) 30 (D) 60

37. Let f : A B be an injective (one-to-one) function. Define g : 2A 2B as:

g(C) = f(x) | x ∈ C, for all subsets C of A.

Define h : 2B 2A as: h(D) = x | x ∈ A, f(x) ∈ D, for all subsets D of B.

Which of the following statements is always true?

(A) g(h(D)) ⊆ D (B) g(h(D)) ⊇ D

(C) g(h(D)) ∩ D = φ (D) g(h(D)) ∩ (B—D) ≠ φ





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38. Consider the set a, b, c with binary operators + and × defined as follows.

For example, a + c = c, c + a = a, c × b = c and b × c = a. Given the following

set of equations:

(a × x) + (a × y) = c

(b × x) + (c × y) = c

The number of solution(s) (i.e., pair(s) (x, y) that satisfy the equations) is

(A) 0 (B) 1 (C) 2 (D) 3

39. Let Σ = a, b, c, d, e be an alphabet. We define an encoding scheme as follows:

g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11.

Let pi denote the i-th prime number (p1 = 2).

For a non-empty string s=a1 ... an, where each ai ∈Σ, define f(s) = ( )1

ig ani iP=Π .

For a non-empty sequence<sj,...,sn>of strings from Σ+,

define ( ) ( )1

if sni n i ih s s P=⟨ ⟩ = ΠK

Which of the following numbers is the encoding, h, of a non-empty sequence of strings?

(A) 7 7 72 3 5 (B) 8 8 82 3 5 (C) 9 9 92 3 5 (D) 10 10 102 5 7

40. A graph G = (V,E) satisfies |E|≤3|V|-6. The min-degree of G is defined as

( ) min degree v V

ν∈

. Therefore, min-degree of G cannot be

(A) 3 (B) 4 (C) 5 (D) 6

41. Consider the following system of linear equations

2 1 4

4 3 12

1 2 8

−

− −

5

7

x

y

z

α

=

Notice that the second and the third columns of the coefficient matrix are linearly

dependent. For how many values of α, does this system of equations have infinitely many solutions?

(A) 0 (B) 1 (C) 2

(D) infinitely many





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42. A piecewise linear function f(x) is plotted using thick solid lines in the figure below (the plot is drawn to scale).

If we use the Newton-Raphson method to find the roots of f(x) =0 using x0, x1, and x2 respectively as initial guesses, the roots obtained would be

(A) 1.3, 0.6, and 0.6 respectively (B) 0.6, 0.6, and 1.3 respectively

(C) 1.3, 1.3, and 0.6 respectively (D) 1.3, 0.6, and 1.3 respectively

43. The following is a scheme for floating point number representation using 16 bits.

Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is:

( ) ( )9 311 1 2 2 , if the exponent 111111

0, otherwise

s em − − − + × ≠

What is the maximum difference between two successive real numbers representable in this system?

(A) 2-40 (B) 2-9 (C) 222 (D) 231

44. A 1-input, 2-output synchronous sequential circuit behaves as follows:

Let zk, nk denote the number of 0’s and 1’s respectively in initial k bits of the input

(zk+nk=k). The circuit outputs 00 until one of the following conditions holds.

• zk – nk=2. In this case, the output at the k-th and all subsequent clock ticks is 10.

Bit Position 15 14 …… 9 8 …… 0

s e m

Sign Exponent Mantissa





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• nk – zk = 2. In this case, the output at the k-th and all subsequent clock ticks is 01.

What is the minimum number of states required in the state transition graph of the above circuit?

(A) 5 (B) 6 (C) 7 (D) 8

45. The literal count of a Boolean expression is the sum of the number of times each

literal appears in the expression. For example, the literal count of (xy + xz’) is 4. What are the minimum possible literal counts of the product-of-sum and sum-of-product representations respectively of the function given by the following Karnaugh map? Here, X denotes “don’t care”

(A) (11, 9) (B) (9, 13) (C) (9, 10) (D) (11, 11)

46. Consider the ALU shown below.

If the operands are in 2’s complement representation, which of the following

operations can be performed by suitably setting the control lines K and C0 only (+ and - denote addition and subtraction respectively)?

(A) A + B, and A - B, but not A + 1 (B) A + B, and A + 1, but not A - B

(C) A + B, but not A – B or A + 1 (D) A + B, and A - B, and A + 1

47. Consider the following circuit composed of XOR gates and non-inverting buffers.





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The non-inverting buffers have delays 1δ = 2 ns and 2δ = 4 ns as shown in the

figure. Both XOR gates and all wires have zero delay. Assume that all gate

inputs, outputs and wires are stable at logic level 0 at time 0. If the following waveform is applied at input A, how many transition(s) (change of logic levels) occur(s) at B during the interval from 0 to 10 ns?

(A) 1 (B) 2 (C) 3 (D) 4

The following information pertains to 48-49:

Consider the following assembly language program for a hypothetical processor

A, B, and C are 8 bit registers. The meanings of various instructions are shown as comments.

MOV B, #0 ; B 0

MOV C, #8 ; C 8

Z: CMP C, #0 ; compare C with 0

JZ X ; jump to X if zero flag is set

SUB C, #1 ; C C - 1

RRC A, #1 ; right rotate A through carry by one bit. Thus:

; if the initial values of A and the carry flag are a7..a0 and

; c0 respectively, their values after the execution of this

; instruction will be c0a7..a1 and a0 respectively.

JC Y ; jump to Y if carry flag is set

JMP Z ; jump to Z

Y: ADD B, #1 ; B B + 1

JMP Z ; jump to Z

X:

48. If the initial value of register A is A0 the value of register B after the program execution will be

(A) the number of 0 bits in A0 (B) the number of 1 bits in A0

(C) A0 (D) 8

49. Which of the following instructions when inserted at location X will ensure that the value of register A after program execution is the same as its initial value?

(A) RRC A, #1

(B) NOP ; no operation

(C) LRC A, #1 ; left rotate A through carry flag by one bit

(D) ADD A, #1





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50. Consider the following deterministic finite state automaton M.

Let S denote the set of seven bit binary strings in which the first, the fourth, and the last bits are 1. The number of strings in S that are accepted by M is

(A) 1 (B) 5 (C) 7 (D) 8

51. Let G = (S,a,b,R,S) be a context free grammar where the rule set R is S a S b | S S | ε


(A) G is not ambiguous

(B) There exist x, y ∈ L(G) such that xy∉ L(G)

(C) There is a deterministic pushdown automaton that accepts L(G)

(D) We can find a deterministic finite state automaton that accepts L(G)

52. Consider two languages L1 and L2, each on the alphabet Σ. Let f: Σ Σ be a

polynomial time computable bijection such that (∀x)[x∈ L1 iff f(x) ∈ L2]. Further,

let f-1 be also polynomial time computable.

Which of the following CANNOT be true?

(A) L1 ∈ P and L2 is finite

(B) L1 ∈ NP and L2 ∈ P

(C) L1 is undecidable and L2 is decidable

(D) L1 is recursively enumerable and L2 is recursive

53. A single tape Turing Machine M has two states q0 and q1, of which q0 is the

starting state. The tape alphabet of M is 0, 1, B and its input alphabet is 0, 1. The symbol B is the blank symbol used to indicate end of an input string. The transition function of M is described in the following table.

The table is interpreted as illustrated below.

The entry (q1, 1, R) in row q0 and column 1 signifies that if M is in state q0 and

reads 1 on the current tape square, then it writes 1 on the same tape square, moves its tape head one position to the right and transitions to state q1.





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Which of the following statements is true about M?

(A) M does not halt on any string in (0+1)+

(B) M does not halt on any string in (00+1)*

(C) M halts on all strings ending in a 0

(D) M halts on all strings ending in a 1

54. Define languages L0 and L1 as follows:

L0 = <M, w, 0> | M halts on w

L1 = <M, w, 1> | M does not halt on w

Here <M, w, i> is a triplet, whose first component, M, is an encoding of a Turing

Machine, second component, w, is a string, and third component, i, is a bit.

Let L = L0∪L1. Which of the following is true?

(A) L is recursively enumerable, but L is not

(B) L is recursively enumerable, but L is not

(C) Both L and L are recursive

(D) Neither L nor L is recursively enumerable

55. Consider the NFA M shown below.

Let the language accepted by M be L. Let L1 be the language accepted by the NFA

M1 obtained by changing the accepting state of M to a non-accepting state and by changing the non-accepting states of M to accepting states. Which of the following statements is true?

(A) L1 = 0,1* - L (B) L1 = 0,1* (C) L1 ⊆ L (D) L1 = L

56. Consider the grammar shown below

S i E t S S′ | a

S′ e S |ε

E b





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In the predictive parse table, M, of this grammar, the entries M[S′ ,e] and

M[S′ ,$] respectively are

(A) S′ e S andS′ε (B) S′ e Sand

(C) S′ ε and S′ ε (D) S′ e S, S′ ε and S′ ε

57. Consider the grammar shown below.

S C C

C c C | d

This grammar is

(A) LL(1) (B) SLR(1) but not LL(1)

(C) LALR(1) but not SLR(1) (D) LR(l) but not LALR(1)

58. Consider the translation scheme shown below.

S T R

R + T print(’+’); R|ε

T num print(num.val);

Here num is a token that represents an integer and num.val represents the

corresponding integer value. For an input string ‘9 + 5 + 2’, this translation scheme will print

(A) 9 + 5 + 2 (B) 9 5 + 2 + (C) 9 5 2 + + (D) + + 9 5 2

59. Consider the syntax directed definition shown below.

S id : = E gen(id.place = E.place;);

E E1 + E2 t = newtemp( );

gen(t = E1.place + E2.place;);

E.place = t;

E id E.place = id.place;

Here, gen is a function that generates the output code, and newtemp is a

function that returns the name of a new temporary variable on every call. Assume that ti’s are the temporary variable names generated by newtemp. For the statement ‘X : = Y + Z’, the 3-address code sequence generated by this definition is

(A) X = Y + Z (B) t1 = Y + Z; X = t1

(C) t1 = Y; t2 = t1 + Z; X = t2 (D) t1 = Y; t2 = Z; t3 = t1 + t2; X = t3

60. A program consists of two modules executed sequentially. Let f1(t) and f2(t)

respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by

(A) ( ) ( )1 2f t f t+ (B) ( ) ( )1 2

0

t

f x f x dx∫





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(C) ( ) ( )1 2

0

t

f x f t x dx−∫ (D) maxf1(t), f2(t)


In a permutation a1 ... an, of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj.

61. If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of 1. . . n?

(A) ( )12

n n − (B)

( )14

n n − (C)

( )14

n n + (D) 2n[log2n]

62. What would be the worst case time complexity of the Insertion Sort algorithm, if the inputs are restricted to permutations of 1. . . n with at most n inversions?

(A) Θ(n2) (B) Θ(n log n) (C) Θ(n1.5) (D) Θ(n)

63. A data structure is required for storing a set of integers such that each of the

following operations can be done in O(log n) time, where n is the number of elements in the set.

I. Deletion of the smallest element

II. Insertion of an element if it is not already present in the set

Which of the following data structures can be used for this purpose?

(A) A heap can be used but not a balanced binary search tree

(B) A balanced binary search tree can be used but not a heap

(C) Both balanced binary search tree and heap can be used

(D) Neither balanced binary search tree nor heap can be used

64. Let S be a stack of size n ≥1. Starting with the empty stack, suppose we push the

first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operations take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m ≥1, define the stack-life of m as the time elapsed from the end of Push(m)

to the start of the pop operation that removes m from S. The average stack-life of an element of this stack is

(A) n(X + Y) (B) 3Y + 2X (C) n(X + Y) - X (D) Y + 2X





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65. Consider the following 2-3-4 tree (i.e., B-tree with a minimum degree of two) in

which each data item is a letter. The usual alphabetical ordering of letters is used in constructing the tree.

What is the result of inserting G in the above tree?

(A)

(B)

(C)






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66. The cube root of a natural number n is defined as the largest natural number m

such that m3≤n. The complexity of computing the cube root of n (n is represented in binary notation) is

(A) O(n) but not O(n0.5)

(B) O(n0.5) but not O((log n)k) for any constant k > 0

(C) O((log n)k) for some constant k > 0, but not O((log log n)m) for any constant m > 0

(D) O((log log n)k) for some constant k > 0.5, but not O((log log n)0.5)

67. Let G = (V,E) be an undirected graph with a subgraph G1 = (V1, E1). Weights are assigned to edges of G as follows.

( ) 10 if e

1 otherwise

Eeω

∈=

A single-source shortest path algorithm is executed on the weighted graph

(V,E,w) with an arbitrary vertex v1 of V1 as the source. Which of the following can always be inferred from the path costs computed?

(A) The number of edges in the shortest paths from v1 to all vertices of G

(B) G1 is connected (C) V1 forms a clique in G

(D) G1 is a tree

68. What is the weight of a minimum spanning tree of the following graph?

(A) 29 (B) 31 (C) 38 (D) 41

69. The following are the starting and ending times of activities A, B, C, D, E, F, G

and H respectively in chronological order: “as bs cs ae ds ce es fs be de gs ee fe hs ge he”. Here, xs denotes the starting time and xe denotes the ending time of activity

X. We need to schedule the activities in a set of rooms available to us. An activity





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can be scheduled in a room only if the room is reserved for the activity for its entire duration. What is the minimum number of rooms required?

(A) 3 (B) 4 (C) 5 (D) 6

70. Let G = (V,E) be a directed graph with n vertices. A path from vi to vj in G is a

sequence of vertices (vi, vi+1, ... , vj) such that (vk, vk+1) ∈ E for all k in i through j - 1. A simple path is a path in which no vertex appears more than once.

Let A be an n x n array initialized as follows.

( )1 if j,k

,0 otherwise

EA j k

∈=

Consider the following algorithm.

for i = 1 to n

for j = 1 to n

for k = 1 to n

A[j,k] = max(A[j,k], A[j,i] + A[i,k]);

Which of the following statements is necessarily true for all j and k after termination of the above algorithm?

(A) A[j,k] ≤ n

(B) If A[j,j] ≥ n - 1, then G has a Hamiltonian cycle

(C) If there exists a path from j to k, A[j,k] contains the longest path length from j to k

(D) If there exists a path from j to k, every simple path from j to k contains at most A[j,k edges

71. Consider the following logic program P

A(x) B(x, y), C(y)

B(x,x)

Which of the following first order sentences is equivalent to P?

(A) (∀x) [(∃y) [B(x,y) ∧ C(y)] ⇒ A(x)] ∧ ¬(∃x)[B(x,x)]

(B) (∀x) [(∀y) [B(x,y) ∧ C(y)] ⇒ A(x)] ∧ ¬(∃x)[B(x,x)]

(C) (∀x) [(∃y) [B(x,y) ∧ C(y)] ⇒ A(x)] ∨ ¬(∃x)[B(x,x)]

(D) (∀x) [(∀y) [B(x,y) ∧ C(y)] ⇒ A(x)] ∧ (∃x)[B(x,x)]

72. The following resolution rule is used in logic programming.

Derive clause (P ∨ Q) from clauses (P ∨ R), (Q ∨ ¬R)

Which of the following statements related to this rule is FALSE?

(A) ((P ∨ R) ^ (Q ∨ ¬R)) ⇒ (P ∨ Q) is logically valid

(B) (P ∨ Q) ⇒ ((P ∨ R) ∧ (Q ∨ ¬R)) is logically valid

(C) (P ∨ Q) is satisfiable if and only if (P ∨ R) ∧ (Q ∨ ¬R) is satisfiable

(D) (P ∨ Q) ⇒ FALSE if and only if both P and Q are unsatisfiable





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The following program fragment is written in a programming language that allows global variables and does not allow nested declarations of functions.

global int i = 100, j = 5;

void P(x)

int i = 10;

print(x + 10);

i = 200;

j = 20;

print (x);

main() P(i + j);

73. If the programming language uses static scoping and call by need parameter passing mechanism, the values printed by the above program are

(A) 115, 220 (B) 25, 220 (C) 25, 15 (D) 115, 105

74. If the programming language uses dynamic scoping and call by name parameter passing mechanism, the values printed by the above program are

(A) 115, 220 (B) 25, 220 (C) 25, 15 (D) 115, 105

75. Consider the following class definitions in a hypothetical Object Oriented

language that supports inheritance and uses dynamic binding. The language should not be assumed to be either Java or C++, though the syntax is similar.

Class P Class Q subclass of P

void f(int i) void f(int i)

print(i); print(2*i);

Now consider the following program fragment:

Px = new Q()

Qy = new Q();

Pz = new Q();

x.f(1); ((P)y).f(1); z.f(1);

Here ((P)y) denotes a typecast of y to P. The output produced by executing the above program fragment will be

(A) 1 2 1 (B) 2 1 1 (C) 2 1 2 (D) 2 2 2





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76. Which of the following is NOT an advantage of using shared, dynamically linked libraries as opposed to using statically linked libraries?

(A) Smaller sizes of executable files

(B) Lesser overall page fault rate in the system

(C) Faster program startup

(D) Existing programs need not be re-linked to take advantage of newer versions of libraries

77. A uni-processor computer system only has two processes, both of which alternate 10 ms CPU bursts with 90 ms I/O bursts. Both the processes were created at

nearly the same time. The I/O of both processes can proceed in parallel. Which of the following scheduling strategies will result in the least CPU utilization (over a long period of time) for this system?

(A) First come first served scheduling

(B) Shortest remaining time first scheduling

(C) Static priority scheduling with different priorities for the two processes

(D) Round robin scheduling with a time quantum of 5 ms

The following information pertains to Q.78-79:

A processor uses 2-level page tables for virtual to physical address translation. Page

tables for both levels are stored in the main memory. Virtual and physical addresses are both 32 bits wide. The memory is byte addressable. For virtual to physical address translation, the 10 most significant bits of the virtual address are used as index into the

first level page table while the next 10 bits are used as index into the second level page table. The 12 least significant bits of the virtual address are used as offset within the page. Assume that the page table entries in both levels of page tables are 4 bytes wide.

Further, the processor has a translation look-aside buffer (TLB), with a hit rate of 96%. The TLB caches recently used virtual page numbers and the corresponding physical page numbers. The processor also has a physically addressed cache with a hit rate of 90%. Main memory access time is 10 ns, cache access time is 1 ns, and TLB access time is also 1 ns.

78. Assuming that no page faults occur, the average time taken to access a virtual address is approximately (to the nearest 0.5 ns)

(A) 1.5 ns (B) 2 ns (C) 3 ns (D) 4 ns

79. Suppose a process has only the following pages in its virtual address space: two contiguous code pages starting at virtual address 0×00000000, two contiguous

data pages starting at virtual address 0×00400000, and a stack page starting at

virtual address 0×FFFFF000. The amount of memory required for storing the page tables of this process is

(A) 8 KB (B) 12 KB (C) 16 KB (D) 20 KB





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The following information pertains to Q.80-81:

Suppose we want to synchronize two concurrent processes P and Q using binary semaphores S and T. The code for the processes P and Q is shown below.

Process P: Process Q:

while (1) while (1)

W: Y:

print ‘0’; print ‘1’;

print ‘0’; print ‘1’;

X: Z:

Synchronization statements can be inserted only at points W, X, Y, and Z

80. Which of the following will always lead to an output staring with ‘001100110011’?

(A) P(S) at W, V(S) at X, P(T) at Y, V(T) at Z, S and T initially 1

(B) P(S) at W, V(T) at X, P(T) at Y, V(S) at Z, S initially 1, and T initially 0

(C) P(S) at W, V(T) at X, P(T) at Y, V(S) at Z, S and T initially 1

(D) P(S) at W, V(S) at X, P(T) at Y, V(T) at Z, S initially 1, and T initially 0

81. Which of the following will ensure that the output string never contains a substring of the form 01n0 or 10n1 where n is odd?

(A) P(S) at W, V(S) at X, P(T) at Y, V(T) at Z, S and T initially 1

(B) P(S) at W, V(T) at X, P(T) at Y, V(S) at Z, S and T initially 1

(C) P(S) at W, V(S) at X, P(S) at Y, V(S) at Z, S initially 1

(D) V(S) at W, V(T) at X, P(S) at Y, P(T) at Z, S and T initially 1

82. The subnet mask for a particular network is 255.255.31.0. Which of the following pairs of IP addresses could belong to this network?

(A) 172.57.88.62 and 172.56.87.233 (B) 10.35.28.2 and 10.35.29.4

(C) 191.203.31.87 and 191.234.31.88 (D) 128.8.129.43 and 128.8.161.55

83. A 2km long broadcast LAN has 107 bps bandwidth and uses CSMA/CD. The signal

travels along the wire at 2×108 m/s. What is the minimum packet size that can be used on this network?

(A) 50 bytes (B) 100 bytes

(C) 200 bytes (D) None of the above

84. Host A is sending data to host B over a full duplex link. A and B are using the

sliding window protocol for flow control. The send and receive window sizes are 5

packets each. Data packets (sent only from A to B) are all 1000 bytes long and the transmission time for such a packet is 50 µs Acknowledgement packets (sent only from B to A) are very small and require negligible transmission time. The





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propagation delay over the link is 200 µs. What is the maximum achievable throughput in this communication?

(A) 7.69 × 106 bps (B) 11.11 × 106 bps

(C) 12.33 × 106 bps (D) 15.00 × 106 bps

85. Consider the following functional dependencies in a database.

Date_of_Birth Age Age Eligibility

Name Roll_number Roll_number Name

Course_number Course_name Course_number Instructor

(Roll_number, Course_number) Grade

The relation (Roll_number, Name, Date_of_birth, Age) is

(A) in second normal form but not in third normal form

(B) in third normal form but not in BCNF

(C) in BCNF (D) in none of the above

86. Consider the set of relations shown below and the SQL query that follows.

Students: (Roll_number, Name, Date_of_birth)

Courses: (Course number, Course_name, Instructor)

Grades: (Roll_number, Course_number, Grade)

select distinct Name

from Students, Courses, Grades

where Students. Roll_number = Grades.Roll_number

and Courses.Instructor = Korth

and Courses.Course_number = Grades.Course_number

and Grades.grade = A

Which of the following sets is computed by the above query?

(A) Names of students who have got an A grade in all courses taught by Korth

(B) Names of students who have got an A grade in all courses

(C) Names of students who have got an A grade in at least one of the courses taught by Korth






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87. Consider three data items D1, D2, and D3, and the following execution schedule

of transactions T1, T2, and T3. In the diagram, R(D) and W(D) denote the actions reading and writing the data item D respectively.


(A) The schedule is serializable as T2; T3; T1

(B) The schedule is serializable as T2; T1; T3

(C) The schedule is serializable as T3; T2; T1

(D) The schedule is not serializable

88. In the following C program fragment, j, k, n and TwoLog_n are integer variables,

and A is an array of integers. The variable n is initialized to an integer ≥3, and

TwoLog_n is initialized to the value of ( )22 * log n

for (k=3; k <= n; k++)

A[k] = 0;

for (k=2; k <= TwoLog_n; k++)

for (j=k+1; j <= n; j++)

A[j] = A[j] || (j%k);

for (j=3; j <= n; j++)

if (!A[j]) printf(”%d ”,j);

The set of numbers printed by this program fragment is

(A) m|m ≤ n, (∃i)[m=i!]

(B) m|m ≤ n, (∃i)[m=i2]

(C) m|m ≤ n, m is prime

(D)





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89. Consider the C program shown below.

#include <stdio.h>

#define print(x) printf(”%d “, x)

int x;

void Q(int z)

z += x; print(z);

void P(int *y)

int x = *y+2;

Q(x); *y = x-1;

print(x);

main(void)

x = 5;

P(&x)

print(x);

The output of this program is

(A) 12 7 6 (B) 22 12 11 (C) 14 6 6 (D) 7 6 6

90. Consider the function f defined below.

struct item

int data;

struct item * next;

;

int f(struct item *p)

return ((p == NULL) || (p ->next == NULL) ||

((p->data <= p -> next -> data) &&

f(p-> next)));

For a given linked list p, the function f returns 1 if and only if

(A) the list is empty or has exactly one element

(B) the elements in the list are sorted in non-decreasing order of data value

(C) the elements in the list are sorted in non-increasing order of data value

(D) not all elements in the list have the same data value

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Q.1 – Q.20 Carry One Mark Each

1. Consider the polynomial ( ) 2 2

0 1 2 3 ,p x a a x a x a x= + + + where 0, .i

a i≠ ∀ The

minimum number of multiplications needed to evaluate pon an input x is:

(A) 3

(B) 4

(C) 6

(D) 9

2. Let X,Y,Z be sets of sizes x, y and z respectively. Let W X Y= × and E be the set of all subsets of W. The number of functions from Z to E is:

(A) 2xy

Z

(B) 2xyZ ×

(C) 2x y

Z+

(D) 2xyz

3. The set 1,2,3,5,7,8,9 under multiplication modulo 10 is not a group. Given

below are four plausible reasons. Which one of them is false?

(A) It is not closed

(B) 2 does not have an inverse

(C) 3 does not have an inverse

(D) 8 does not have an inverse

4. A relation R is defined on ordered pairs of integers as follows:

( ) ( ), ,x y R u v if and .x u y v< > Then R is:

(A) Neither a Partial Order nor an Equivalence Relation

(B) A Partial Order but not a Total Order

(C) A Total Order

(D) An Equivalence Relation

5. For which one of the following reasons does Internet Protocol (IP) use the time-

to-live (TTL) field in the IP datagram header?

(A) Ensure packets reach destination within that time

(B) Discard packets that reach later than that time

(C) Prevent packets from looping indefinitely

(D) Limit the time for which a packet gets queued in intermediate routers.

6. Consider three CPU-intensive processes, which require 10, 20 and 30 time units

and arrive at times 0, 2 and 6, respectively. How many context switches are




needed if the operating system implements a shortest remaining time first

scheduling algorithm? Do not count the context switches at time zero and at the

end.

(A) 1

(B) 2

(C) 3

(D) 4

7. Consider the following grammar.

*S S E

S E

E F E

E F

F id

→

→

→ +

→

→

Consider the following ( )0LR items corresponding to the grammar above.

(i) *.S S E→

(ii) .E F E→ +

(iii) .E F E→ +

Given the items above, which two of them will appear in the same set in the

canonical sets-of-items for the grammar?

(A) (i) and (ii)

(B) (ii) and (iii)

(C) (i) and (iii)


8. You are given a free running clock with a duty cycle of 50% and a digital

waveform f which changes only at the negative edge of the clock. Which one of

the following circuits (using clocked D flip-flops) will delay the phase of f by

180°?

(A)

(B)

f

clk

D Q

D Q

f

clk

D D Q Q




(C)

(D)

9. A CPU has 24-bit instructions. A program starts at address 300 (in decimal).

Which one of the following is a legal program counter (all values in decimal)?

(A) 400

(B) 500

(C) 600

(D) 700

10. In a binary max heap containing n numbers, the smallest element can be found

in time

(A) ( )O n

(B) ( )logO n

(C) ( )loglogO n

(D) ( )1O

11. Consider a weighted complete graph G on the vertex set 1 2, ,...., nν ν ν such that

the weight of the edge ( ), is 2 - .i j i jν ν The weight of a minimum spanning tree

of G is:

(A) 1n −

(B) 2 2n −

(C) 2

n

(D) 2n

12. To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it

runs in linear time, the data structure to be used is:

(A) Queue

f

clk

D D Q Q

f

clk

D Q

D Q




(B) Stack

(C) Heap

(D) B-Tree

13. A scheme for storing binary trees in an array X is as follows. Indexing of X starts

at 1 instead of 0. the root is stored at X[1]. For a node stored at X[i], the left

child, if any, is stored in X[2i] and the right child, if any, in X[2i+1]. To be able to store any binary tree on n vertices the minimum size of X should be

(A) 2

log n

(B) n

(C) 2 1n +

(D) 2 1n −

14. Which one of the following in place sorting algorithms needs the minimum

number of swaps?

(A) Quick sort

(B) Insertion sort

(C) Selection sort

(D) Heap sort

15. Consider the following C-program fragment in which , and ni j are integer

variables.

( )for i = n, j = 0; i > 0; i /= 2, j +=i ;

Let ( )val j denote the value stored in the variable j after termination of the

for loop. Which one of the following is true?

(A) ( ) ( )logval j nθ=

(B) ( ) ( )val j nθ=

(C) ( ) ( )val j nθ=

(D) ( ) ( )logval j n nθ=

16. Let S be an NP-complete problem and Q and R be two other problems not known

to be in NP. Q is polynomial time reducible to S and S is polynomial-time

reducible to R. Which one of the following statements is true?

(A) R is NP-complete

(B) R is NP-hard

(C) Q is NP-complete

(D) Q is NP-hard




17. An element in an array X is called a leader if it is greater than all elements to the

right of it in X. The best algorithm to find all leaders in an array

(A) Solves it in linear time using a left to right pass of the array

(B) Solves it in linear time using a right to left pass of the array

(C) Solves it using divide and conquer in time ( )logn nθ

(D) Solves it in time ( )2nθ

18. We are given a set 1,...... where 2 .in iX x x x= = A sample S X⊆ is drawn by

selecting each i

x independently with probability 1.

2ip = The expected value of the

smallest number in sample S is:

(A) 1

n

(B) 2

(C) n

(D) n

19. Let 1 20 1 0 , 0 , 0 1 0 , 0 ,n m n m n m n m mL n m L n m+ + += ≥ = ≥ and

30 1 0 , 0 .n m n m n mL n m+ + += ≥ Which of these languages are NOT context free?

(A) 1

L only

(B) 3

L only

(C) 1 2 and L L

(D) 2 3 and L L

20. Consider the following log sequence of two transactions on a bank account, with

initial balance 12000, that transfer 2000 to a mortgage payment and then apply a 5% interest.

1. T1 start

2. T1 B old=1200 new=10000

3. T1 M old=0 new=2000

4. T1 commit

5. T2 start

6. T2 B old=10000 new=10500

7. T2 commit

Suppose the database system crashes just before log record 7 is written. When the system is restarted, which one statement is true of the recovery procedure?

(A) We must redo log record 6 to set B to 10500

(B) We must undo log record 6 to set B to 10000 and then redo log records 2

and 3




(C) We need not redo log records 2 and 3 because transaction T1 has committed

(D) We can apply redo and undo operations in arbitrary order because they are

idempotent.

Q.21 – Q.75 Carry Two Marks Each

21. For each element in a set of size 2 ,n an unbiased coin is tossed. The 2n coin

tosses are independent. An element is chosen if the corresponding coin toss were

head. The probability that exactly n elements are chosen is:

(A)

2

4n

n

n

(B)

2

2n

n

n

(C) 1

2n

n

(D) 1

2

22. Let E, F and G be finite sets.

Let ( ) ( ) ( )( ) ( ) and .X E F F G Y E E G E F= − = − − −I I I

Which one of the following is true?

(A) X Y⊂

(B) X Y⊃

(C) X Y=

(D) and X Y Y X− ≠ ∅ − ≠ ∅

23. F is an n n× real matrix. b is an 1n × real vector. Suppose there are two

1n × vectors, and u ν such that ,u ν≠ and , .Fu b F bν= = Which one of the

following statements is false?

(A) Determinant of F is zero

(B) There are an infinite number of solutions to Fx = b

(C) There is an 0x ≠ such that 0Fx =

(D) F must have two identical rows

24. Given a set of elements 1,2,.....,N n= and two arbitrary subsets

and ,A N B N⊆ ⊆ how many of the !n permutations π from N to N satisfy

( )( ) ( )( )min min ,A Bπ π= where ( )min S is the smallest integer in the set of




integers ( ), and S Sπ is the set of integers obtained by applying permutation π to

each element of ?S

(A) ( )n A B A B− U

(B) ( )2 2 2A B n+

(C) !A B

nA B

I

U

(D) 2 n

A BA B

IU

25. Let 1,2,3,........, , 3.S m m= > Let 1......

nX X be subsets of S each of size 3.

Define a function f from S to the set of natural numbers as, ( )f i is the number of

sets jX that contain the element .i That is ( ) .jf i j i X= ∈

Then ( )1

m

i

f i=∑ is:

(A) 3m

(B) 3n

(C) 2 1m +

(D) 2 1n +

26. Which one of the first order predicate calculus statements given below correctly

expresses the following English statement?

Tigers and lions attack if they are hungry or threatened.

(A) ( ) ( )( ) ( ) ( )( ) ( ) tiger lion hungry threatened attacksx x x x x x ∀ ∧ → ∨ →

(B) ( ) ( )( ) ( ) ( )( ) ( ) tiger lion hungry threatened attacksx x x x x x ∀ ∨ → ∨ ∧

(C) ( ) ( )( ) ( ) ( ) ( )( ) tiger lion attacks hungry threatenedx x x x x x ∀ ∨ → → ∨

(D) ( ) ( )( ) ( ) ( )( ) ( ) tiger lion hungry threatened attacksx x x x x x ∀ ∨ → ∨ →

27. Consider the following propositional statements:

( )( )) ( ) ( )( )( )( )) ( ) ( )( )

1:

2 :

P A B C A C B C

P A B C A C B C

∧ → ≡ → ∧ →

∨ → ≡ → ∨ →


(A) P1 is a tautology, but not P2

(B) P2 is a tautology, but not P1

(C) P1 and P2 are both tautologies

(D) Both P1 and P2 are not tautologies




28. A logical binary relation , is defined as follows:

A B A B

True True True

True False True

False True False

False False True

Let ~be the unary negation (NOT) operator, with higher precedence then .

Which one of the following is equivalent to ?A B∧

(A) ( )~ A B

(B) ( )~ ~A B

(C) ( )~ ~ ~A B

(D) ( )~ ~ A B

29. If s is a string over ( )*0 1+ then let ( )0n s denote the number of 0’s in

( )1 and s n s the number of 1’s in .s Which one of the following languages is not

regular?

(A) ( ) ( ) 00 1 * is a 3-digit primeL s n s= ∈ +

(B) ( ) ( ) ( ) 0 10 1 * for every prefix of , 2L s s s n s n s′ ′ ′= ∈ + − ≤

(C) ( ) ( ) ( ) 0 10 1 * 4L s n s n s= ∈ + − ≤

(D) ( ) ( ) ( ) 0 10 1 * mod 7 mod 5 0L s n s n s= ∈ + = =

30. For ( )0 1 *S ∈ + let ( )d s denote the decimal value of s (e.g. ( )101 5d = ).

Let ( ) ( ) ( ) 0 1 * mod5 2 and mod7 4L s d s d s= ∈ + = ≠

Which one of the following statements is true?

(A) L is recursively enumerable, but not recursive

(B) L is recursive, but not context-free

(C) L is context-free, but not regular

(D) L is regular

31. Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph

( ),G V E= with V divisible by 3 and DHAM3 be the problem of determining if a

Hamiltonian cycle exists in such graphs. Which one of the following is true?




(A) Both DHAM3 and SHAM3 are NP-hard

(B) SHAM3 is NP-hard, but DHAM3 is not

(C) DHAM3 is NP-hard, but SHAM3 is not

(D) Neither DHAM3 nor SHAM3 is NP-hard

32. Consider the following statements about the context free grammar

, , ,G S SS S ab S ba S= → → → →∈

I. G is ambiguous

II. G produces all strings with equal number of a’s and b’s

III. G can be accepted by a deterministic PDA.

Which combination below expresses all the true statements about G?

(A) I only

(B) I and III only

(C) II and III only

(D) I, II and III

33. Let 1

L be a regular language, 2

L be a deterministic context-free language and 3

L a

recursively enumerable, but not recursive, language. Which one of the following statements is false?

(A) 1 2

L LI is a deterministic CFL

(B) 3 1

L LI is recursive

(C) 1 2

L LU is context free

(D) 1 2 3

L L LI I is recursively enumerable

34. Consider the regular language ( )111 11111 *.L = + The minimum number of

states in any DFA accepting this languages is:

(A) 3

(B) 5

(C) 8

(D) 9

35.

x

y

z

x

y

MUX

MUX f

0

1

0

1




Consider the circuit above. Which one of the following options correctly

represents ( ), , ?f x y z

(A) xz xy yz+ +

(B) xz xy yz+ +

(C) xz xy yz+ +

(D) xz xy yz+ +

36. Given two three bit numbers 2 1 0 2 1 0

and and ,a a a b b b c the carry in, the function

that represents the carry generate function when these two numbers are added

is:

(A) 2 2 2 1 1 2 1 0 0 2 0 1 0 1 2 1 1 0 2 0 0 2 1 0

a b a a b a a a b a a b b a b b a a b b a b b b+ + + + + +

(B) 2 2 2 1 0 2 1 1 0 1 0 2 1 1 0 2 1 0 2 0 2 0 1 0

a b a b b a a b b a a b b a a b a a b b a a b b+ + + + + +

(C) ( ) ( ) ( )( )2 2 2 2 1 1 1 1 0 0a b a b a b a b a b+ + ⊕ + + ⊕ +

(D) 2 2 2 1 1 2 1 0 0 2 0 1 0 1 2 1 1 0 2 0 0 2 1 0a b a a b a a a b a a b b a b b a a b b a b b b+ + + + + +

37. Consider the circuit in the diagram. The ⊕ operator represents Ex-OR. The D flip-

flops are initialized to zeroes (cleared).

The following data: 100110000 is supplied to the “data” terminal in nine clock

cycles. After that the values of 2 1 0

q q q are:

(A) 000

(B) 001

(C) 010

(D) 101

38. Consider a Boolean function ( ), , , .f w x y z suppose that exactly one of its inputs is

allowed to change at a time. If the function happens to be true for two input

vectors 1 1 1 1 1, , ,i w x y z= and 2 2 2 2 2, , , ,i w x y z= we would like the function to

remain true as the input changes from

( )1 2 1 2 to and differ in exactly one bit position ,i i i i without becoming false

Q D Q D Q D

clk clk clk

clock

data

q0 q1 q2




momentarily. Let ( ) ( ), , , 5,7,11,12,13,15 .f w x y z = ∑ Which of the following cube

covers of f will ensure that the required property is satisfied?

(A) , , , ,wxz wxy xyz xyz wyz

(B) , ,wxy wxz wyz

(C) , ,wxyz xz wxyz

(D) , , , , ,wzy wyz wxz wxz xyz xyz

39. We consider the addition of two 2’s complement numbers 1 2 0

....n n

b b b− − and

1 2 0

.... .n n

a a a− − A binary adder for adding unsigned binary numbers is used to add

the two numbers. The sum is denoted by 1 2 0

....n n

c c c− − and the carry-out by .out

c

Which one of the following options correctly identifies the overflow condition?

(A) ( )1 1out n nc a b− −⊕

(B) 1 1 1 1 1 1n n n n n na b c a b c− − − − − −+

(C) 1out n

c c −⊕

(D) 1 1 1n n n

a b c− − −⊕ ⊕

40. Consider numbers represented in 4-bit gray code. Let 3 2 1 0

h h h h be the gray code

representation of a number n and let 3 2 1 0

g g g g be the gray code of

( )1n + ( )modulo 16 value of the number. Which one of the following functions is

correct?

(A) ( ) ( )0 3 2 1 0 1,2,3,6,10,13,14,15g h h h h = ∑

(B) ( ) ( )1 3 2 1 0 4,9,10,11,12,13,14,15g h h h h = ∑

(C) ( ) ( )2 3 2 1 0 2,4,5,6,7,12,13,15g h h h h = ∑

(D) ( ) ( )3 3 2 1 0 0,1,6,7,10,11,12,13g h h h h = ∑

41. A CPU has a cache with block size 64 bytes. The main memory has k banks, each bank being c bytes wide. Consecutive c − byte chunks are mapped on

consecutive banks with wrap-around. All the k banks can be accessed in parallel, but two accesses to the same bank must be serialized. A cache block access may

involve multiple iterations of parallel bank accesses depending on the amount of

data obtained by accessing all the k banks in parallel. Each iteration requires

decoding the bank numbers to be accessed in parallel and this takes .2

kns The

latency of one bank access is 80 ns. If 2 and 24,c k= = the latency of retrieving

a cache block starting at address zero from main memory is:

(A) 92 ns

(B) 104 ns

(C) 172 ns




(D) 184 ns

42. A CPU has a five-stage pipeline and runs at 1 GHz frequency. Instruction fetch

happens in the first stage of the pipeline. A conditional branch instruction

computes the target address and evaluates the condition in the third stage of the

pipeline. The processor stops fetching new instructions following a conditional

branch until the branch outcome is known. A program executes 910 instructions

out of which 20% are conditional branches. If each instruction takes one cycle to

complete on average, the total execution time of the program is:

(A) 1.0 second

(B) 1.2 seconds

(C) 1.4 seconds

(D) 1.6 seconds

43. Consider a new instruction named branch-on-bit-set (mnemonic bbs). The

instruction “bbs reg, pos, label” jumps to label if bit in position pos of register

operand reg is one. A register is 32 bits wide and the bits are numbered 0 to 31,

bit in position 0 being the least significant. Consider the following emulation of this instruction on a processor that does not have bbs implemented.

temp ← reg & mask

Branch to label if temp is non-zero.

The variable temp is a temporary register. For correct emulation, the variable

mask must be generated by

(A) 0 1mask pos← ×

(B) 0mask ffffffff pos← ×

(C) mask pos←

(D) 0mask f← ×

44. Station A uses 32 byte packets to transmit messages to Station B using a sliding

window protocol. The round trip delay between A and B is 80 milliseconds and

the bottleneck bandwidth on the path between A and B is 128 kbps. What is the optimal window size that A should use?

(A) 20

(B) 40

(C) 160

(D) 320

45. Two computers C1 and C2 are configured as follows. C1 has IP address

203.197.2.53 and netmask 255.255.128.0. C2 has IP address 203.197.75.201

and netmask 255.255.192.0. which one of the following statements is true?




(A) C1 and C2 both assume they are on the same network

(B) C2 assumes C1 is on same network, but C1 assumes C2 is on a different

network

(C) C1 assumes C2 is on same network, but C2 assumes C1 is on a different

network

(D) C1 and C2 both assume they are on different networks.

46. Station A needs to send a message consisting of 9 packets to Station B using a

sliding window (window size 3) and go-back-n error control strategy. All packets

are ready and immediately available for transmission. If every 5th packet that A

transmits gets lost (but no acks from B ever get lost), then what is the number of

packets that A will transmit for sending the message to B?

(A) 12

(B) 14

(C) 16

(D) 18

47. Consider the following graph:

Which one of the following cannot be the sequence of edges added, in that

order, to a minimum spanning tree using Kruskal’s algorithm?

(A) ( ) ( ) ( ) ( ) ( ), , , ,a b d f b f d c d e− − − − −

(B) ( ) ( ) ( ) ( ) ( ), , , ,a b d f d c b f d e− − − − −

(C) ( ) ( ) ( ) ( ) ( ), , , ,d f a b d c b f d e− − − − −

(D) ( ) ( ) ( ) ( ) ( ), , , ,d f a b b f d e d c− − − − −

a

b d

f

e c

1

6

3 2

4

3

4

1

5

7

2




48. Let T be a depth first search tree in an undirected graph G. Vertices and u ν are leaves of this tree .T The degrees of both and u ν in G are at least 2. which one of the following statements is true?

(A) There must exist a vertex w adjacent to both and u ν in G

(B) There must exist a vertex w whose removal disconnects and u ν in G

(C) There must exist a cycle in G containing and u ν

(D) There must exist a cycle in G containing u and all its neighbours in G.

49. An implementation of a queue Q, using two stacks S1 and S2, is given below:

void insert (Q, x)

push (S1, x);

void delete (Q)

if (stack-empty(S2)) then

if (stack-empty(S1)) then

print(“Q is empty”);

return;

else while (!(stack-empty(S1)))

x=pop(S1);

push(S2,x);

x=pop(S2);

Let n insert and ( )m n≤ delete operations be performed in an arbitrary order

on an empty queue Q. Let and x y be the number of push and pop operations

performed respectively in the process. Which one of the following is true for all and ?m n

(A) 2 and 2n m x n m y n m+ ≤ < ≤ ≤ +

(B) 2 and 2 2n m x n m y n+ ≤ < ≤ ≤

(C) 2 2 and 2m x n m y n m≤ < ≤ ≤ +

(D) 2 2 and 2 2m x n m y n≤ < ≤ ≤

50. A set X can be represented by an array x n as follows:

1 if

0 otherwise

i Xx i

∈=

Consider the following algorithm in which , and zx y are Boolean arrays of size n:

algorithm zzz(x[ ], y[ ], z [ ] )

int i;




for(i=0;i<n;++i)

z[i] = (x[i] ∧ ~y[i]) ∨ (~x[i] ∧ y[i])

The set Z computed by the algorithm is:

(A) ( )X YU

(B) ( )X YI

(C) ( ) ( )X Y Y X− −I

(D) ( ) ( )X Y Y X− −U

51. Consider the following recurrence:

( ) ( ) ( )2 1, 1 1T n T n T = + =


(A) ( ) ( )loglogT n nθ=

(B) ( ) ( )logT n nθ=

(C) ( ) ( )T n nθ=

(D) ( ) ( )T n nθ=

52. The median of n elements can be found in ( )O n time. Which one of the following

is correct about the complexity of quick sort, in which median is selected as

pivot?

(A) ( )nθ

(B) ( )logn nθ

(C) ( )2nθ

(D) ( )3nθ

53. Consider the following C-function in which and a n b m are two sorted integer

arrays and c n m+ be another integer array.

void xyz(int a[], int b [], int c [])

int i,j,k;

i=j=k=0;

while ((i<n) && (j<m))

if (a[i] < b[j]) c[k++] = a[i++];

else c[k++] = b[j++];




Which of the following condition(s) hold(s) after the termination of the while

loop?

(i) , 1, and 1 if j m k n j a n b j i n< = + − − < =

(ii) , 1, and 1 if i n k m i b m a i j m< = + − − ≤ =

(A) only (i)

(B) only (ii)

(C) either (i) or (ii) but not both

(D) neither (i) nor (ii)

54. Given two arrays of numbers 1 1,..., and ,...,

n na a b b where each number is 0 or 1,

the fastest algorithm to find the largest span ( ),i j such that

1 1... ... ,i i j i i ja a a b b b+ ++ + + = + + + or report that there is not such span,

(A) Takes ( ) ( )n3 and 2nO Ω time if hashing is permitted

(B) Takes ( ) ( )3 2.5 and O n nΩ time in the key comparison model

(C) Takes ( )nΘ time and space

(D) Takes ( )O n time only if the sum of the 2n elements is an even number

55. Consider these two functions and two statements S1 and S2 about them.

S1: The transformation form work1 to work2 is valid, i.e., for any program state

and input arguments, work2 will compute the same output and have the same

effect on program state as work1

S2: All the transformations applied to work1 to get work2 will always improve the

performance (i.e reduce CPU time) of work2 compared to work1

(A) S1 is false and S2 is false

(B) S1 is false and S2 is true

(C) S1 is true and S2 is false

(D) S1 is true and S2 is true

int work1(int *a, int i, int j) int work2(int *a, int i, int j)

int x = a[i+2]; int t1 = i+2;

a[j] = x+1; int t2 = a[t1];

return a[i+2] – 3; a[j] = t2+1;

return t2 – 3;




56. Consider the following code written in a pass-by-reference language like

FORTRAN and these statements about the code.

subroutine swap(ix,iy)

it = ix

L1 : ix = iy

L2 : iy = it

end

ia = 3

ib = 8

call swap (ia, 1b+5)

print *, ia, ib

end

S1: The compiler will generate code to allocate a temporary nameless cell,

initialize it to 13, and pass the address of the cell swap

S2: On execution the code will generate a runtime error on line L1

S3: On execution the code will generate a runtime error on line L2

S4: The program will print 13 and 8

S5: The program will print 13 and -2

Exactly the following set of statement(s) is correct:

(A) S1 and S2

(B) S1 and S4

(C) S3

(D) S1 and S5

57. Consider this C code to swap two integers and these five statements: the code

void swap (int *px, int *py)

*px = *px - *py;

*py = *px + *py;

*px = *py - *px;

S1: will generate a compilation error

S2: may generate a segmentation fault at runtime depending on the arguments

passed

S3: correctly implements the swap procedure for all input pointers referring to

integers stored in memory locations accessible to the process




S4: implements the swap procedure correctly for some but not all valid input

pointers

S5: may add or subtract integers and pointers.

(A) S1

(B) S2 and S3

(C) S2 and S4

(D) S2 and S5

58. Consider the following grammar:

*

S FR

R S

F id

ε

→

→

→

In the predictive parser table, M, of the grammar the entries

, and ,$M S id M R respectively.

(A) and S FR R ε→ →

(B) and S FR→

(C) and *S FR R S→ →

(D) and F id R ε→ →

59. Consider the following translation scheme.

( )

( ) ( ) ( )

* print '*' ;

print '+' ;

print id.value ;

S ER

R E R

E F E F

F S id

ε

→

→

→ +

→

Here id is a token that represents an integer and .id value represents the

corresponding integer value. For an input '2 *3 4',+ this translation scheme

prints

(A) 2 *3 4+

(B) 2 * 3 4+

(C) 2 3 * 4 +

(D) 2 3 4+*

60. Consider the following C code segment.

for (i – 0, i<n; i++)

for (j=0; j<n; j++)

if (i%2)

x += (4*j + 5*i);

y += (7 + 4*j);




Which one of the following is false?

(A) The code contains loop invariant computation

(B) There is scope of common sub-expression elimination in this code

(C) There is scope of strength reduction in this code

(D) There is scope of dead code elimination in this code

61. The atomic fetch-and-set x, y instruction unconditionally sets the memory

location x to 1 and fetches the old value of x n y without allowing any intervening

access to the memory location x. consider the following implementation of P and

V functions on a binary semaphore .S

void P (binary_semaphore *s)

unsigned y;

unsigned *x = &(s->value);

do

fetch-and-set x, y;

while (y);

void V (binary_semaphore *s)

S->value = 0;


(A) The implementation may not work if context switching is disabled in P

(B) Instead of using fetch-and –set, a pair of normal load/store can be used

(C) The implementation of V is wrong

(D) The code does not implement a binary semaphore

62. A CPU generates 32-bit virtual addresses. The page size is 4 KB. The processor

has a translation look-aside buffer (TLB) which can hold a total of 128 page table entries and is 4-way set associative. The minimum size of the TLB tag is:

(A) 11 bits

(B) 13 bits

(C) 15 bits

(D) 20 bits

63. A computer system supports 32-bit virtual addresses as well as 32-bit physical

addresses. Since the virtual address space is of the same size as the physical

address space, the operating system designers decide to get rid of the virtual memory entirely. Which one of the following is true?

(A) Efficient implementation of multi-user support is no longer possible




(B) The processor cache organization can be made more efficient now

(C) Hardware support for memory management is no longer needed

(D) CPU scheduling can be made more efficient now

64. Consider three processes (process id 0, 1, 2 respectively) with compute time

bursts 2, 4 and 8 time units. All processes arrive at time zero. Consider the

longest remaining time first (LRTF) scheduling algorithm. In LRTF ties are broken

by giving priority to the process with the lowest process id. The average turn

around time is:

(A) 13 units

(B) 14 units

(C) 15 units

(D) 16 units

65. Consider three processes, all arriving at time zero, with total execution time of

10, 20 and 30 units, respectively. Each process spends the first 20% of execution

time doing I/O, the next 70% of time doing computation, and the last 10% of

time doing I/O again. The operating system uses a shortest remaining compute

time first scheduling algorithm and schedules a new process either when the

running process gets blocked on I/O or when the running process finishes its

compute burst. Assume that all I/O operations can be overlapped as much as possible. For what percentage of time does the CPU remain idle?

(A) 0%

(B) 10.6%

(C) 30.0%

(D) 89.4%

66. Consider the following snapshot of a system running n processes. Process i is holding

ix instances of a resource R, 1 .i n≤ ≤ currently, all instances of R are

occupied. Further, for all ,i process i has placed a request for an additional

i

y instances while holding the i

x instances it already has. There are exactly two

processes and p q such that 0.p qy y= = Which one of the following can serve as

a necessary condition to guarantee that the system is not approaching a deadlock?

(A) ( ) ,min , maxp q k p q kx x y≠<

(B) ,minp q k p q kx x y≠+ ≥

(C) ( )max , 1p qx x >

(D) ( )min , 1p qx x >

67. Consider the relation account (customer, balance) where customer is a primary

key and there are no null values. We would like to rank customers according to

decreasing balance. The customer with the largest balance gets rank 1. ties are




not broke but ranks are skipped: if exactly two customers have the largest balance they each get rank 1 and rank 2 is not assigned.

select A.customer, count(B.customer)

Query1: from account A, account B

where A.balance <=B.balance

group by A.customer

select A.customer, 1+count(B.customer)

Query2: from account A, account B

where A.balance < B.balance

group by A.customer

Consider these statements about Query1 and Query2.

1. Query1 will produce the same row set as Query2 for some but not all

databases.

2. Both Query1 and Query2 are correct implementation of the specification

3. Query1 is a correct implementation of the specification but Query2 is not

4. Neither Query1 nor Query2 is a correct implementation of the specification

5. Assigning rank with a pure relational query takes less time than scanning in

decreasing balance order assigning ranks using ODBC.

Which two of the above statements are correct?

(A) 2 and 5

(B) 1 and 3

(C) 1 and 4

(D) 3 and 5

68. Consider the relation enrolled (student, course) in which (student, course) is the

primary key, and the relation paid (student, amount) where student is the

primary key. Assume no null values and no foreign keys or integrity constraints. Given the following four queries:

Query1:select student from enrolled where student in (select student from paid)

Query2:select student from paid where student in (select student from enrolled)

Query3:select E.student from enrolled E, paid P where E.student = P.student

Query4:select student from paid where exists

(select * from enrolled where enrolled.student = paid.student)

Which one of the following statements is correct?

(A) All queries return identical row sets for any database

(B) Query2 and Query4 return identical row sets for all databases but there exist

databases for which Query1 and Query2 return different row sets.

(C) There exist databases for which Query3 returns strictly fewer rows than

Query2




(D) There exist databases for which Query4 will encounter an integrity violation

at runtime.

69. Consider the relation enrolled (student, course) in which (student, course) is the

primary key, and the relation paid (student, amount) where student is the

primary key. Assume no null values and no foreign keys or integrity constraints.

Assume that amounts 6000, 7000, 8000, 9000 and 10000 were each paid by

20% of the students. Consider these query plans (Plan 1 on left, Plan 2 on right) to “list all courses taken by students who have paid more than x”

A disk seek takes 4ms, disk data transfer bandwidth is 300 MB/s and checking a

tuple to see if amount is greater than x takes 10µs. Which of the following statements is correct?

(A) Plan 1 and Plan 2 will not output identical row sets for all databases

(B) A course may be listed more than once in the output of Plan 1 for some

databases

(C) For x = 5000, Plan 1 executes faster than Plan 2 for all databases

(D) For x = 9000, Plan I executes slower than Plan 2 for all databases.

70. The following functional dependencies are given:

, , , , , .AB CD AF D DE F C G F E G A→ → → → → →

Which one of the following options is false?

(A) CF ACDEFG+

=

(B) BG ABCDG+

=

(C) AF ACDEFG+

=

(D) AB ABCDFG+

=

Probe index on student

Sequential scan, select amount > x

Indexed nested loop join

Project on course

enrolled paid

Probe index on student

Sequential scan

Indexed nested loop join

Select on amount > x

Project on course

enrolled paid




Common Data Questions:

Common Data for Questions 71, 72, 73:

The 2n vertices of a graph G corresponds to all subsets of a set of size n, for 6n ≥ . Two

vertices of G are adjacent if and only if the corresponding sets intersect in exactly two

elements.

71. The number of vertices of degree zero in G is:

(A) 1

(B) n

(C) 1n +

(D)2n

72. The maximum degree of a vertex in G is:

(A) 222

2

nn

(B) 22n−

(C) 32 3n− ×

(D) 12n−

73. The number of connected components in G is:

(A) n

(B) 2n +

(C) 22n

(D) 2n

n

Common Data for Questions 74, 75:

Consider two cache organizations: The first one is 32 KB 2-way set associative with 32-

byte block size. The second one is of the same size but direct mapped. The size of an

address is 32 bits in both cases. A 2-to-1 multiplexer has a latency of 0.6 ns while a k-bit comparator has a latency of 10k ns. The hit latency of the set associative

organization is 1

h while that of the direct mapped one is 2.h

74. The value of 1

h is:

(A) 2.4 ns

(B) 2.3 ns

(C) 1.8 ns

(D) 1.7 ns

75. The value of 2

h is:

(A) 2.4 ns




(B) 2.3 ns

(C) 1.8 ns

(D) 1.7 ns

Linked Answer Questions: Q.76 to Q85 Carry Two Marks Each

Statement for Linked Answer Questions 76 & 77:

A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3

children. A 3-ary heap can be represented by an array as follows: The root is stored in

the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to

a[3]. The nodes from the second level of the tree from left to right are stored from a[4]

location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property.

76. Which one of the following is a valid sequence of elements in an array

representing 3-ary max heap?

(A) 1, 3, 5, 6, 8, 9

(B) 9, 6, 3, 1, 8, 5

(C) 9, 3, 6, 8, 5, 1

(D) 9, 5, 6, 8, 3, 1

77. Suppose the elements 7, 2, 10 and 4 are inserted, in that order, into the valid 3-

ary max heap found in the above question, Q.76. Which one of the following is the sequence of items in the array representing the resultant heap?

(A) 10, 7, 9, 8, 3, 1, 5, 2, 6, 4

(B) 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

(C) 10, 9, 4, 5, 7, 6, 8, 2, 1, 3

(D) 10, 8, 6, 9, 7, 2, 3, 4, 1, 5


Barrier is a synchronization construct where a set of processes synchronizes globally i.e.

each process in the set arrives at the barrier and waits for all others to arrive and then

all processes leave the barrier. Let the number of processes in the set be three and S be

a binary semaphore with the usual P and V functions. Consider the following C implementation of a barrier with line numbers shown on left.

void barrier (void)




1: P(S);

2: process_arrived++;

3. V(S);

4: while (process_arrived !=3);

5: P(S);

6: process_left++;

7: if (process_left==3)

8: process_arrived = 0;

9: process_left = 0;

10:

11: V(S);

The variables process_arrived and process_left are shared among all processes and are

initialized to zero. In a concurrent program all the three processes call the barrier function when they need to synchronize globally.

78. The above implementation of barrier is incorrect. Which one of the following is true?

(A) The barrier implementation is wrong due to the use of binary semaphore S

(B) The barrier implementation may lead to a deadlock if two barrier in

invocations are used in immediate succession.

(C) Lines 6 to 10 need not be inside a critical section

(D) The barrier implementation is correct if there are only two processes instead of three.

79. Which one of the following rectifies the problem in the implementation?

(A) Lines 6 to 10 are simply replaced by process_arrived--

(B) At the beginning of the barrier the first process to enter the barrier waits

until process_arrived becomes zero before proceeding to execute P(S).

(C) Context switch is disabled at the beginning of the barrier and re-enabled at

the end.

(D) The variable process_left is made private instead of shared


A CPU has a 32 KB direct mapped cache with 128-byte block size. Suppose A is a two-

dimensional array of size 512×512 with elements that occupy 8-bytes each. Consider the following two C code segments, P1 and P2.

P1: for (i=0; i<512; i++)

for (j=0; j<512; j++)

x +=A[i] [j];




P2: for (i=0; i<512; i++)

for (j=0; j<512; j++)

x +=A[j] [i];

P1 and P2 are executed independently with the same initial state, namely, the array A is

not in the cache and , ,i j x are in registers. Let the number of cache misses experienced

by P1 be 1

M and that for P2 be 2.M

80. The value of 1

M is:

(A) 0

(B) 2048

(C) 16384

(D) 262144

81. The value of the ratio 1

2

M

Mis:

(A) 0

(B) 1

16

(C) 1

8

(D) 16


Consider the diagram shown below where a number of LANs are connected by

(transparent) bridges. In order to avoid packets looping through circuits in the graph,

the bridges organize themselves in a spanning tree. First, the root bridge is identified as

the bridge with the least serial number. Next, the root sends out (one or more) data

units to enable the setting up of the spanning tree of shortest paths from the root bridge

to each bridge.

Each bridge identifies a port (the root port) through which it will forward frames to the

root bridge. Port conflicts are always resolved in favour of the port with the lower index

value. When there is a possibility of multiple bridges forwarding to the same LAN (but

not through the root port), ties are broken as follows: bridges closest to the root get

preference and between such bridges, the one with the lowest serial number is

preferred.




82. For the given connection of LANs by bridges, which one of the following choices

represents the depth first traversal of the spanning tree of bridges?

(A) B1, B5, B3, B4, B2

(B) B1, B3, B5, B2, B4

(C) B1, B5, B2, B3, B4

(D) B1, B3, B4, B5, B2

83. Consider the correct spanning tree for the previous question. Let host H1 send

out a broadcast ping packet. Which of the following options represents the

correct forwarding table on B3?

(A) (B)

Hosts Port

H1, H2, H3, H4 3

H5, H6, H9, H10 1

B1

H1 H2 H3 H4 1 2

2 3 4

1 4

B5 B3

1 2

3

H5 H6 H7 H8

B4 B2

2 1 2

1

3 3

H9 H10 H11 H12




H7, H8, H11, H12 2

(C) (D)


84. Which one of the following grammars generates the language ?i jL a b i j= ≠

(A) (B) S aS Sb a b→

S AC CB

C aC b a b

A a A

B B b

→

→

→ ∈

→ ∈

(C) (D)

S AC CB

C aC b

A a A

B B b

→

→ ∈

→ ∈

→ ∈

S AC CB

C aC b

A a A a

B B b b

→

→ ∈

→

→

85. In the correct grammar above, what is the length of the derivation (number of

steps starring from S) to generate the string l ma b with l m≠ ?

(A) ( )max , 2l m +

(B) 2l m+ +

(C) 3l m+ +

(D) ( )max , 3l m +

Hosts Port

H1, H2 4

H3, H4 3

H5, H6 1

H7, H8, H9, H10,H11,H12 2

Hosts Port

H3, H4 3

H5, H6, H9, H10 1

H1, H2 4

H7, H8, H11, H12 2

Hosts Port

H1, H2, H3, H4 3

H5, H7, H9, H10 1

H7, H8, H11, H12 4

CSGATE Paper 2007 www.gateforum.com




1. Consider the following two statements about the function ( ) :f x x=

P. ( )f x is continuous for all real values of x

Q. ( )f x is differentiable for all real values of x

Which of the following is TRUE?

(A) P is true and Q is false. (B) P is false and Q is true.

(C) Both P and Q are true. (D) Both P and Q are false.

2. Let S be a set of n elements. The number of ordered pairs in the largest and the

smallest equivalence relations on S are:

(A) n and n (B) 2n and n (C) 2n and 0 (D) n and 1

3. What is the maximum number of different Boolean functions involving n Boolean

variables?

(A) 2n (B) 2n (C) 22n

(D) 2

2n

4. Let G be the non-planar graph with the minimum possible number of edges. Then

G has

(A) 9 edges and 5 vertices (B) 9 edges and 6 vertices

(C) 10 edges and 5 vertices (D) 10 edges and 6 vertices

5. Consider the DAG with 1,2,3,4,5,6 ,V = shown below.

Which of the following is NOT a topological ordering?

(A) 1 2 3 4 5 6 (B) 1 3 2 4 5 6 (C) 1 3 2 4 6 5 (D) 3 2 4 1 6 5

6. Which of the following problems is undecidable?

(A) Membership problem for CFGs. (B) Ambiguity problem for CFGs.

(C) Finiteness problem for FSAs. (D) Equivalence problem for FSAs.

2 5

1

3

4

6




7. Which of the following is TRUE?

(A) Every subset of a regular set is regular.

(B) Every finite subset of a non-regular set is regular.

(C) The union of two non-regular sets is not regular.

(D) Infinite union of finite sets is regular.

8. How many 3-to-8 line decoders with an enable input are needed to construct a 6-

to-64 line decoder without using any other logic gates?

(A) 7 (B) 8 (C) 9 (D) 10

9. Consider the following Boolean function of four variables:

( ) ( ), , , 1,3,4,6,9,11,12,14f w x y z = ∑

The function is:

(A) independent of one variables. (B) independent of two variables.

(C) independent of three variables. (D) dependent on all the variables.

10. Consider a 4-way set associative cache consisting of 128 lines with a line size of

64 words. The CPU generates a 20-bit address of a word in main memory. The number of bits in the TAG, LINE and WORD fields are respectively:

(A) 9, 6, 5 (B) 7, 7, 6 (C) 7, 5, 8 (D) 9, 5, 6

11. Consider a disk pack with 16 surfaces, 128 tracks per surface and 256 sectors

per track. 512 bytes of data are stored in a bit serial manner in a sector. The

capacity of the disk pack and the number of bits required to specify a particular sector in the disk are respectively:

(A) 256 Mbyte, 19 bits (B) 256 Mbyte, 28 bits

(C) 512 Mbyte, 20 bits (D) 64 Gbyte, 28 bits

12. The height of a binary tree is the maximum number of edges in any root to leaf

path. The maximum number of nodes in a binary tree of height h is:

(A) 2 1h − (B) 12 1h− − (C) 12 1h+ − (D) 12h+

13. The maximum number of binary trees that can be formed with three unlabeled

nodes is:

(A) 1 (B) 5 (C) 4 (D) 3

14. Which of the following sorting algorithms has the lowest worst-case complexity?

(A) Merge sort (B) Bubble sort (C) Quick sort (D) Selection sort




15. Consider the following segment of C-code:

int j, n;

j = 1;

while (j <=n)

j = j*2;

The number of comparisons made in the execution of the loop for any n > 0 is:

(A) 2log 1n + (B) n (C) 2log n (D) 2log 1n +

16. Group 1 contains some CPU scheduling algorithms and Group 2 contains some

applications. Match entries in Group 1 to entries in Group 2.

(A) P - 3 Q - 2 R - 1 (B) P - 1 Q - 2 R - 3

(C) P - 2 Q - 3 R - 1 (D) P - 1 Q - 3 R - 2

17. Consider the following statements about user level threads and kernel level

threads. Which one of the following statements is FALSE?

(A) Context switch time is longer for kernel level threads than for user level

threads.

(B) User level threads do not need any hardware support.

(C) Related kernel level threads can be scheduled on different processors in a

multi-processor system.

(D) Blocking one kernel level thread blocks all related threads.

18. Which one of the following is a top-down parser?

(A) Recursive descent parser. (B) Operator precedence parser.

(C) An LR(k) parser. (D) An LALR(k) parser.

19. In Ethernet when Manchester encoding is used, the bit rate is:

(A) Half the baud rate. (B) Twice the baud rate.

(C) Same as the baud rate. (D) None of the above

20. Which one of the following uses UDP as the transport protocol?

(A) HTTP (B) Telnet (C) DNS (D) SMTP

Group I Group II

(P) Gang Scheduling (1) Guaranteed Scheduling

(Q) Rate Monotonic Scheduling (2) Real-time Scheduling

(R) Fair Share Scheduling (3) Thread Scheduling





21. How many different non-isomorphic Abelian groups of order 4 are there?

(A) 2 (B) 3 (C) 4 (D) 5

22. Let Graph(x) be a predicate which denotes that x is a graph. Let Connected(x) be

a predicate which denotes that x is connected. Which of the following first order

logic sentences DOES NOT represent the statement: “Not every graph is connected”?

(A) ( ) ( )( )x Graph x Connected x¬∀ ⇒ (B) ( ) ( )( )x Graph x Connected x∃ ∧ ¬

(C) ( ) ( )( )x Graph x Connected x¬∀ ¬ ∨ (D) ( ) ( )( )x Graph x Connected x∀ ⇒ ¬

23. Which of the following graphs has an Eulerian circuit?

(A) Any k-regular graph where k is an even number.

(B) A complete graph on 90 vertices.

(C) The complement of a cycle on 25 vertices.


24. Suppose we uniformly and randomly select a permutation from the 20!

Permutations of 1, 2,3 ,…..,20. What is the probability that 2 appears at an

earlier position than any other even number in the selected permutation?

(A) 1

2 (B)

1

10 (C)

9!

20! (D) None of these

25. Let A be a 4 × 4 matrix with eigenvalues -5, -2, 1, 4. Which of the following is an

eigenvalue of ,A I

I A

where I is the 4 × 4 identity matrix?

(A) -5 (B) -7 (C) 2 (D) 1

26. Consider the set , , , .S a b c d= Consider the following 4 partitions 1 2 3 4, , ,π π π π on

1 2 3 4: , , , , , , , , .S abcd ab cd abc d a b c dπ π π π= = = = Let p be the partial

order on the set of partitions 1 2 3 4, , ,S π π π π′ = defined as follows: i jπ πp if and

only if iπ refines .jπ The poset diagram for ( ),S′ p is:

(A) (B)

1π

2π

3π

4π

1π

2π

3π

4π




(C) (D)

27. Consider the set of (column) vectors defined by

31 2 3 1 2 30, where , , .

TTX x R x x x x x x x= ∈ + + = = Which of the following is

TRUE?

(A) 1, 1,0 , 1,0, 1T T

− − is a basis for the subspace X.

(B) 1, 1,0 , 1,0, 1T T

− − is a linearly independent set, but it does not span X and

therefore is not a basis of X.

(C) X is not a subspace of 3R


28. Consider the series 1 0

9, 0.5

2 8n

nn

xx x

x+ = + = obtained from the Newton-Raphson

method. The series converges to

(A) 1.5 (B) 2 (C) 1.6 (D) 1.4

29. A minimum state deterministic finite automaton accepting the language

*0,1 , number of 0s and 1s in are divisible by 3 and 5, respectivelyL w w w= ∈

has

(A) 15 states (B) 11 states (C) 10 states (D) 9 states

30. The language 0 21 0i iL i= ≥ over the alphabet 0,1,2 is:

(A) not recursive

(B) is recursive and is a deterministic CFL.

(C) is a regular language.

(D) is not a deterministic CFL but a CFL.

1π

2π

4π

3π

3π

2π

1π

4π




31. Which of the following languages is regular?

(A) 0,1Rww w+∈ (B) , 0,1Rww x x w

+∈

(C) , 0,1Rwxw x w+∈ (D) , 0,1Rxww x w

+∈

32. Let ( ) ( ), , , 0,4,5,7,8,9,13,15 .f w x y z = ∑ Which of the following expressions are

NOT equivalent to f ?

(P) x y z w xy wy z xz′ ′ ′ ′ ′ ′+ + +

(Q) w y z wx y xz′ ′ ′ ′ ′+ +

(R) w y z wx y xyz xy z′ ′ ′ ′ ′ ′+ + +

(S) x y z wx y w y′ ′ ′ ′ ′ ′+ +

(A) P only (B) Q and S (C) R and S (D) S only

33. Define the connective * for the Boolean variables X and Y as: X * Y = XY + .X Y′ ′ Let * .Z X Y= Consider the following expressions P, Q and R.

π : * : * : * * 1P X Y Z Q Y X Z R X Y Z= = =


(A) Only P and Q are valid. (B) Only Q and R are valid.

(C) Only P and R are valid. (D) All P, Q, R are valid.

34. Suppose only one multiplexer and one inverter are allowed to be used to

implement any Boolean function of n variables. What is the minimum size of the multiplexer needed?

(A) 2n line to 1 line (B) 12n+ line to 1 line

(C) 12n− line to 1 line (D) 22n− line to 1 line

35. In a look-ahead carry generator, the carry generate function iG and the carry

propagate function iP for inputs iA and iB are given by:

and i i i i i iP A B G AB= ⊕ =

The expressions for the sum bit iS and the carry bit 1iC + of the look-ahead carry

adder are given by:

1 0 and , where is the input carry.i i i i i i iS P C C G PC C+= ⊕ = +

Consider a two-level logic implementation of the look-ahead carry generator.

Assume that all i and GiP are available for the carry generator circuit and that

the AND and OR gates can have any number of inputs. The number of AND gates

and OR gates needed to implement the look-ahead carry generator for a 4-bit

adder with 3 2 1 0 4, , , and S S S S C as its outputs are respectively:

(A) 6, 3 (B) 10, 4 (C) 6, 4 (D) 10, 5




36. The control signal functions of a 4-bit binary counter are given below (where X is

“don’t care”):

Clear Clock Load Count Function

1 X X X Clear to 0

0 X 0 0 No change

0 ↑ 1 X Load input

0 ↑ 0 1 Count next

The counter is connected as follows:

Assume that the counter and gate delays are negligible. If the counter starts at

0, then it cycles through the following sequence:

(A) 0, 3, 4 (B) 0, 3, 4, 5

(C) 0, 1, 2, 3, 4 (D) 0, 1, 2, 3, 4, 5

37. Consider a pipelined processor with the following four stages:

IF: Instruction Fetch

ID: Instruction Decode and Operand Fetch

EX: Execute

WB: Write Back

The IF, ID and WB stages take one clock cycle each to complete the operation.

The number of clock cycles for the EX stage depends on the instruction. The ADD

and SUB instructions need 1 clock cycle and the MUL instruction needs 3 clock

cycles in the EX stage. Operand forwarding is used in the pipelined processor.

What is the number of clock cycles taken to complete the following sequence of

instructions?

ADD R2, R1, R0 R2 R1 + R0

MUL R4, R3, R2 R4 R3 * R2

SUB R6, R5, R4 R6 R5 − R4

Clear

Inputs

0 0 1 1

4-bit counter

4A 3A 2A 1A

Count=1

Load=0

Clock




(A) 7 (B) 8 (C) 10 (D) 14

38. The following postfix expression with single digit operands is evaluated using a stack:

8 2 3 / 2 3 * + 5 1 * -∧

Note that ∧ is the exponentiation operator. The top two elements of the stack

after the first * is evaluated are:

(A) 6, 1 (B) 5, 7 (C) 3, 2 (D) 1, 5

39. The inorder and preorder traversal of a binary tree are

d b e a f c g and a b d e c f g, respectively

The postorder traversal of the binary tree is:

(A) d e b f g c a (B) e d b g f c a (C) e d b f g c a (D) d e f g b c a

40. Consider a hash table of size seven, with starting index zero, and a hash function

( )3 4 mod7.x + Assuming the hash table is initially empty, which of the following

is the contents of the table when the sequence 1, 3, 8, 10 is inserted into the table using closed hashing? Note that − denotes an empty location in the table.

(A) 8, −, −, −, −, −, 10 (B) 1, 8, 10, −, −, −, 3

(C) 1, −, −, −, −, −, 3 (D) 1, 10, 8, −, −, −, 3

41. In an unweighted, undirected connected graph, the shortest path from a node S

to every other node is computed most efficiently, in terms of time complexity, by

(A) Dijkstra’s algorithm starting from S.

(B) Warshall’s algorithm

(C) Performing a DFS starting from S.

(D) Performing a BFS starting from S.

42. Consider the following C function:

int f(int n)

static int r = 0;

if (n <= 0) return 1;

if (n > 3)

r = n;

return f(n-2)+2;

return f(n-1)+r;

What is the value of ( )5 ?f

(A) 5 (B) 7 (C) 9 (D) 18




43. A complete n-ary tree is a tree in which each node has n children or no children.

Let I be the number of internal nodes and L be the number of leaves in a

complete n-ary tree. If L = 41, and I = 10, what is the value of n?

(A) 3 (B) 4 (C) 5 (D) 6

44. In the following C function, let n ≥ m.

int gcd(n,m)

if (n%m ==0) return m;

n = n%m;

return gcd(m,n);

How many recursive calls are made by this function?

(A) ( )2log nΘ (B) ( )nΩ (C) ( )2 2log log nΘ (D) ( )nΘ

45. What is the time complexity of the following recursive function:

int DoSomething (int n)

if (n <= 2)

return 1;

else

return (DoSomething (floor(sqrt(n))) + n);

(A) ( )2nΘ (B) ( )2logn nΘ (C) ( )2log nΘ (D) ( )2 2log log nΘ

46. Consider the following C program segment where CellNode represents a node in a

binary tree:

struct CellNode

struct CellNOde *leftChild;

int element;

struct CellNode *rightChild;

;

int GetValue (struct CellNode *ptr)

int value = 0;

if (ptr != NULL)

if ((ptr->leftChild == NULL) &&

(ptr->rightChild == NULL))

value = 1;

else

value = value + GetValue(ptr->leftChild)




+ GetValue(ptr->rightChild);

return(value);

The value returned by GetValue when a pointer to the root of a binary tree is

passed as its argument is:

(A) the number of nodes in the tree

(B) the number of internal nodes in the tree

(C) the number of leaf nodes in the tree

(D) the height of the tree

47. Consider the process of inserting an element into a Max Heap, where the Max

Heap is represented by an array. Suppose we perform a binary search on the

path from the new leaf to the root to find the position for the newly inserted element, the number of comparisons performed is:

(A) ( )2log nΘ (B) ( )2 2log log nΘ (C) ( )nΘ (D) ( )2logn nΘ

48. Which of the following is TRUE about formulae in Conjunctive Normal Form?

(A) For any formula, there is a truth assignment for which at least half the

clauses evaluate to true.

(B) For any formula, there is a truth assignment for which all the clauses evaluate to true.

(C) There is a formula such that for each truth assignment, at most one-fourth of

the clauses evaluate to true.

(D) None of the above.

49. Let w be the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weight w . Which of the following is FALSE?

(A) There is a minimum spanning tree containing .e

(B) If e is not in a minimum spanning tree T, then in the cycle formed by adding

e to T, all edges have the same weight.

(C) Every minimum spanning tree has an edge of weight w .

(D) e is present in every minimum spanning tree.

50. An array of n numbers is given, where n is an even number. The maximum as

well as the minimum of these n numbers needs to be determined. Which of the following is TRUE about the number of comparisons needed?

(A) At least 2n c− comparisons, for some constant ,c are needed.

(B) At most 1.5 2n − comparisons are needed.

(C) At least 2logn n comparisons are needed.





51. Consider the following C code segment:

int IsPrime(n)

int i,n;

for(i=2;i<=sqrt(n);i++)

if(n%i == 0)

printf(“Not Prime\n”); return 0;

return 1;

Let ( )T n denote the number of times the for loop is executed by the program on

input n. Which of the following is TRUE?

(A) ( ) ( ) ( ) ( ) and T n O n T n n= = Ω (B) ( ) ( ) ( ) ( ) and 1T n O n T n= = Ω

(C) ( ) ( ) ( ) ( ) and T n O n T n n= = Ω (D) None of the above

52. Consider the grammar with non-terminals 1, , ,N S C S= terminals

, , , , ,T a b i t e= with S as the start symbol, and the following set of rules:

1

1

S iCtSS a

S eS

C b

ε

→

→

→

The grammar is NOT LL(1) because:

(A) it is left recursive (B) it is right recursive

(C) it is ambiguous (D) it is not context-free.

53. Consider the following two statements:

P: Every regular grammar is LL(1)

Q: Every regular set has a LR(1) grammar


(A) Both P and Q are true (B) P is true and Q is false

(C) P is false and Q is true (D) Both P and Q are false

54. In a simplified computer the instructions are:

jOP R , iR - Performs j iR OP R and stores the result in register .iR

OP m, iR - Performs val iOP R and stores the result in .iR val

denotes the content of memory location m.

MOV , im R - Moves the content of memory location m to register .iR

MOV ,iR m - Moves the content of register iR to memory location m.

The computer has only to registers, and OP is either ADD or SUB. Consider the

following basic block:




1

2

3 2

4 1 3

t a b

t c d

t e t

t t t

= +

= +

= −

= −

Assume that all operands are initially in memory. The final value of the

computation should be in memory. What is the minimum number of MOV instructions in the code generated for this basic block?

(A) 2 (B) 3 (C) 5 (D) 6

55. An operating system uses Shortest Remaining Time first (SRT) process

scheduling algorithm. Consider the arrival times and execution times for the following processes:

Process Execution time Arrival time

P1 20 0

P2 25 15

P3 10 30

P4 15 45

What is the total waiting time for process P2?

(A) 5 (B) 15 (C) 40 (D) 55

56. A virtual memory system uses First In First Out (FIFO) page replacement policy

and allocates a fixed number of frames to a process. Consider the following

statements:

P: Increasing the number of page frames allocated to a process sometimes

increases the page fault rate.

Q: Some programs do not exhibit locality of reference.

Which one of the following is TRUE?

(A) Both P and Q are true, and Q is the reason for P

(B) Both P and Q are true, but Q is not the reason for P.

(C) P is false, but Q is true

(D) Both P and Q are false.

57. A single processor system has three resource types X, Y and Z, which are shared

by three processes. There are 5 units of each resource type. Consider the

following scenario, where the column alloc denotes the number of units of each

resource type allocated to each process, and the column request denotes the

number of units of each resource type requested by a process in order to

complete execution. Which of these processes will finish LAST?




(A) P0 (B) P1 (C) P2

(D) None of the above, since the system is in a deadlock.

58. Two processes, P1 and P2, need to access a critical section of code. Consider the

following synchronization construct used by the processes:

Here, wants1 and wants2 are shared variables, which are initialized to false.

Which one of the following statements is TRUE about the above construct?

(A) It does not ensure mutual exclusion.

(B) It does not ensure bounded waiting.

(C) It requires that processes enter the critical section in strict alternation.

(D) It does not prevent deadlocks, but ensures mutual exclusion.

59. Information about a collection of students is given by the relation

studinfo(studId, name, sex). The relation enroll(studId, courseId) gives which

student has enrolled for (or taken) what course(s). Assume that every course is

taken by at least one male and at least one female student. What does the following relational algebra expression represent?

( )( ) ( )( )( )courseId studId "female" courseIdstudInfo enroll enrollsexσ =Π Π × Π −

(A) Courses in which all the female students are enrolled.

(B) Courses in which a proper subset of female students are enrolled.

(C) Courses in which only male students are enrolled.


alloc request

X Y Z X Y Z

P0 1 2 1 1 0 3

P1 2 0 1 0 1 2

P2 2 2 1 1 2 0

/* P1 */

while (true)

wants1 = true;

while (wants2==true);

/* Critical

Section */

wants1=false;

/* Remainder section */

/* P2 */

while (true)

wants2 = true;

while (wants1==true);

/* Critical

Section */

Wants2=false;

/* Remainder section */




60. Consider the relation employee(name, sex, supervisorName) with name as the

key. supervisorName gives the name of the supervisor of the employee under

consideration. What does the following Tuple Relational Calculus query produce?

( ) e.name employee e ∧

( ) ( ) employee x .supervisorName e.name x.sex = "male" x x ∀ ¬ ∨ ≠ ∨

(A) Names of employees with a male supervisor.

(B) Names of employees with no immediate male subordinates.

(C) Names of employees with no immediate female subordinates.

(D) Names of employees with a female supervisor.

61. Consider the table employee(empId, name, department, salary) and the two

queries 1 2,Q Q below. Assuming that department 5 has more than one employee,

and we want to find the employees who get higher salary than anyone in the

department 5, which one of the statements is TRUE for any arbitrary employee table?

1 :Q Select e.empId

From employee e

Where not exists

(Select * From employee s where s.department = “5” and s.salary >=e.salary)

2 :Q Select e.empId

From employee e

Where e.salary > Any

(Select distinct salary From employee s Where s.department = “5”)

(A) 1Q is the correct query

(B) 2Q is the correct query

(C) Both 1 2 and Q Q produce the same answer.

(D) Neither 1 2 nor Q Q is the correct query

62. Which one of the following statements if FALSE?

(A) Any relation with two attributes is in BCNF

(B) A relation in which every key has only one attribute is in 2NF

(C) A prime attribute can be transitively dependent on a key in a 3 NF relation.

(D) A prime attribute can be transitively dependent on a key in a BCNF relation.

63. The order of a leaf node in a treeB+ − is the maximum number of (value, data

record pointer) pairs it can hold. Given that the block size is 1K bytes, data

record pointer is 7 bytes long, the value field is 9 bytes long and a block pointer is 6 bytes long, what is the order of the leaf node?

(A) 63 (B) 64 (C) 67 (D) 68




64. Consider the following schedules involving two transactions. Which one of the

following statements is TRUE?

( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )

1 1 1 2 2 2 1

2 1 2 2 2 1 1

: ; ; ; ; ;

: ; ; ; ; ;

S r X r Y r X r Y w Y w X

S r X r X r Y w Y r Y w X

(A) Both 1 2 and S S are conflict serializable.

(B) 1S is conflict serializable and 2S is not conflict serializable.

(C) 1S is not conflict serializable and 2S is conflict serializable.

(D) Both 1 2 and S S are not conflict serializable.

65. There are n stations in a slotted LAN. Each station attempts to transmit with a

probability p in each time slot. What is the probability that ONLY one station transmits in a given time slot?

(A) ( ) 11

nnp p

−− (B) ( ) 1

1n

p−

− (C) ( ) 11

np p

−− (D) ( ) 1

1 1n

p−

− −

66. In a token ring network the transmission speed is 710 bps and the propagation

speed is 200 metres/µs. The 1-bit delay in this network is equivalent to:

(A) 500 metres of cable. (B) 200 metres of cable.

(C) 20 metres of cable. (D) 50 metres of cable.

67. The address of a class B host is to be split into subnets with a 6-bit subnet

number. What is the maximum number of subnets and the maximum number of

hosts in each subnet?

(A) 62 subnets and 262142 hosts. (B) 64 subnets and 262142 hosts.

(C) 62 subnets and 1022 hosts. (D) 64 subnets and 1024 hosts.

68. The message 11001001 is to be transmitted using the CRC polynomial 3 1x + to protect it from errors. The message that should be transmitted is:

(A) 11001001000 (B) 11001001011

(C) 11001010 (D) 110010010011

69. The distance between two stations M and N is L kilometers. All frames are K bits

long. The propagation delay per kilometer is t seconds. Let R bits/second be the

channel capacity. Assuming that processing delay is negligible, the minimum

number of bits for the sequence number field in a frame for maximum utilization,

when the sliding window protocol is used, is:

(A) 2

2 2log

LtR K

K

+

(B) 2

2log

LtR

K

(C) 2

2log

LtR K

K

+

(D) 2

2log

2

LtR K

K

+




70. Match the following:

(P) SMTP (1) Application layer

(Q) BGP (2) Transport layer

(R) TCP (3) Data link layer

(S) PPP (4) Network layer

(5) Physical layer

(A) P - 2 Q - 1 R - 3 S - 5

(B) P - 1 Q - 4 R - 2 S - 3

(C) P - 1 Q - 4 R - 2 S - 5

(D) P - 2 Q - 4 R - 1 S - 3

Common Data Questions

Common Data for Questions 71, 72, 73:

Consider the following program segment. Here R1, R2 and R3 are the general purpose

registers.

Instruction Operation Instruction size (no.of words)

MOV R1, (3000) R1 m[3000] 2

LOOP: MOV R2, (R3) R2 M[R3] 1

ADD R2, R1 R2 R1 + R2 1

MOV (R3), R2 M[R3] R2 1

INC R3 R3 R3 + 1 1

DEC R1 R1 R1 – 1 1

BNZ LOOP Branch on not zero 2

HALT Stop 1

Assume that the content of memory location 3000 is 10 and the content of the register

R3 is 2000. The content of each of the memory locations from 2000 to 2010 is 100. The program is loaded from the memory location 1000. All the numbers are in decimal.

71. Assume that the memory is word addressable. The number of memory references

for accessing the data in executing the program completely is:

(A) 10 (B) 11 (C) 20 (D) 21

72. Assume that the memory is word addressable. After the execution of this

program, the content of memory location 2010 is:

(A) 100 (B) 101 (C) 102 (D) 110




73. Assume that the memory is byte addressable and the word size is 32 bits. If an

interrupt occurs during the execution of the instruction “INC R3”, what return address will be pushed on to the stack?

(A) 1005 (B) 1020 (C) 1024 (D) 1040

Common Data for Questions 74, 75:

Consider the following Finite State Automaton:

74. The language accepted by this automaton is given by the regular expression

(A) * * * *b ab ab ab (B) ( )*a b+ (C) ( )**b a a b+ (D) * * *b ab ab

75. The minimum state automaton equivalent to the above FSA has the following

number of states

(A) 1 (B) 2 (C) 3 (D) 4

Linked Answer Questions: Q.76 to Q.85 Carry Two Marks Each


Suppose the letters a, b, c, d, e, f have probabilities 1 1 1 1 1 1, , , , , ,

2 4 8 16 32 32 respectively.

76. Which of the following is the Huffman code for the letter a, b, c, d, e, f?

(A) 0, 10, 110, 1110, 11110, 11111

(B) 11, 10, 011, 010, 001, 000

(C) 11, 10, 01, 001, 0001, 0000

(D) 110, 100, 010, 000, 001, 111

77. What is the average length of the correct answer to Q.76?

(A) 3 (B) 2.1875 (C) 2.25 (D) 1.9375


Consider the CFG with , ,S A B as the non-terminal alphabet, ,a b as the terminal

alphabet, S as the start symbol and the following set of production rules:

a

q0 q1 q2

b b

a

a

q3

a

b

b




S aB S bA

B b A a

B bS A aS

B aBB S bAA

→ →

→ →

→ →

→ →

78. Which of the following strings is generated by the grammar?

(A) aaaabb (B) aabbbb (C) aabbab (D) abbbba

79. For the correct answer strings to Q.78, how many derivation trees are there?

(A) 1 (B) 2 (C) 3 (D) 4


Consider a machine with a byte addressable main memory of 162 bytes. Assume that a

direct mapped data cache consisting of 32 lines of 64 bytes each is used in the system.

A 50 × 50 two-dimensional array of bytes is stored in the main memory starting from

memory location 1100H. Assume that the data cache is initially empty. The complete

array is accessed twice. Assume that the contents of the data cache do not change in between the two accesses.

80. How many data cache misses will occur in total?

(A) 48 (B) 50 (C) 56 (D) 59

81. Which of the following lines of the data cache will be replaced by new blocks in

accessing the array for the second time?

(A) line 4 to line 11 (B) line 4 to line 12

(C) line 0 to line 7 (D) line 0 to line 8


A process has been allocated 3 page frames. Assume that none of the pages of the

process are available in the memory initially. The process makes the following sequence of page references (reference string): 1, 2, 1, 3, 7, 4, 5, 6, 3, 1

82. If optimal page replacement policy is used, how many page faults occur for the

above reference string?

(A) 7 (B) 8 (C) 9 (D) 10

83. Least Recently Used (LRU) page replacement policy is a practical approximation

to optimal page replacement. For the above reference string, how many more page faults occur with LRU than with the optimal page replacement policy?

(A) 0 (B) 1 (C) 2 (D) 3





Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move

either one unit up or one unit right, i.e., if it is at ( ),i j then it can move to either

( )1,i j+ or ( ), 1 .i j +

84. How many distinct paths are there for the robot to reach the point (10,10)

starting from the initial position (0,0)?

(A) 20

10

(B) 202

(C) 102 (D) None of the above

85. Suppose that the robot is not allowed to traverse the line segment from (4,4) to

(5,4). With this constraint, how many distinct paths are there for the robot to reach (10,10) starting from (0,0)?

(A) 92 (B) 192

(C) 8 11

4 5

×

(D)

20 8 11

10 4 5

− ×

CS GATE Paper 2008 www.gateforum.com




1. x

x sinxlim equals

x cos x→∞

−+

(A) 1 (B) -1 (C) ∞ (D) −∞

2. If P, Q, R are subsets of the universal set U, then

( ) ( )c c cP Q R P Q R Q R∩ ∩ ∪ ∩ ∩ ∪ ∪ is

(A) c cQ R∪ (B) c cP Q R∪ ∪ (C) c c cP Q R∪ ∪ (D) U

3. The following system of equations

1 2 3

1 2 3

1 2 3

x x 2x 1

x 2x 3x 2

x 4x x 4

+ + =

+ + =

+ + α =

has a unique solution. The only possible value(s) for α is/are

(A) 0 (B) either 0 or 1

(C) one of 0, 1 or -1 (D) any real number

4. In the IEEE floating point representation the hexadecimal value 0x00000000

corresponds to

(A) The normalized value 2-127 (B) The normalized value 2-126

(C) The normalized value +0 (D) The special value +0

5. In the Karnaugh map shown below, X denotes a don’t care term. What is the

minimal form of the function represented by the Karnaugh map?

(A) b.d a.d+ (B) a.b b.d a.b.d+ + (C) b.d a.b.d+ (D) a.b b.d a.d+ +

6. Let r denote number system radix. The only value(s) of r that satisfy the

equation r r121 11 is / are=

(A) decimal 10 (B) decimal 11

(C) decimal 10 and 11 (D) any value >2

1 1 1

X

X

1 X1

00 01 1011

abcd

00

01

11

10




7. The most efficient algorithm for finding the number of connected components in

an undirected graph on n vertices and m edges has time complexity

(A) ( )nΘ (B) ( )mΘ (C) ( )m nΘ + (D) ( )mnΘ

8. Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit

( )( )

( )

1

3

2

f m 4,5,6,7,8

f m 1,6,15

f m 1,6,8,15

then f is

= Σ

= Σ

= Σ

(A) ( )m 4,6Σ (B) ( )m 4,8Σ (C) ( )m 6,8Σ (D) ( )m 4,6,8Σ

9. Which of the following is true for the language pa p is a prime ?

(A) It is not accepted by a Turing Machine

(B) It is regular but not context-free

(C) It is context-free but not regular

(D) It is neither regular nor context-free, but accepted by a Turing machine

10. Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite

II. Whether a given context-free language is regular

III. Whether two push-down automata accept the same language

IV. Whether a given grammar is context-free

(A) I and II (B) I and IV (C) II and III (D)II and IV

11. Which of the following describes a handle (as applicable to LR-parsing)

appropriately?

(A) It is the position in a sentential form where the next shift or reduce operation

will occur

(B) It is non-terminal whose production will be used for reduction in the next

step

(C) It is a production that may be used for reduction in a future step along with a

position in the sentential form where the next shift or reduce operation will

occur

(D) It is the production p that will be used for reduction in the next step along

with a position in the sentential form where the right hand side of the production may be found

f2f

1f

3f




12. Some code optimizations are carried out on the intermediate code because

(A) They enhance the portability of the compiler to other target processors

(B) Program analysis is more accurate on intermediate code than on machine code

(C) The information from dataflow analysis cannot otherwise be used for

optimization

(D) The information from the front end cannot otherwise be used for optimization

13. If L and L are recursively enumerable then L is

(A) regular (B) context-free

(C) context-sensitive (D) recursive

14. What is the maximum size of data that the application layer can pass on to the

TCP layer below?

(A) Any size (B) 216 bytes-size of TCP header

(C) 216 bytes (D) 1500 bytes

15. Which of the following tuple relational calculus expression(s) is/are equivalent to

( )( )t r P t ?∀ ∈

( )( )( )( )

( )( )( )( )

I. t r P t

II. t r P t

III. t r P t

IV. t r P t

¬∃ ∈

∃ ∉

¬∃ ∈ ¬

∃ ∉ ¬

(A) I only (B) II only

(C) III only (D) III and IV only

16. A clustering index is defined on the fields which are of type

(A) non-key and ordering (B) non-key and non-ordering

(C) key and ordering (D) key and non-ordering

17. Which of the following system calls results in the sending of SYN packets?

(A) socket (B) bind (C) listen (D) connect

18. Which combination of the integer variables x, y and z makes the variable a get

the value 4 in the following expression?

( ) ( )( ) ( )( )a x y ? x z ?x : z : y z ?y : z= > > >

(A) x 3,y 4,z 2= = = (B) x 6,y 5,z 3= = =

(C) x 6,y 3,z 5= = = (D) x 5,y 4,z 5= = =




19. The Breadth First Search algorithm has been implemented using the queue data

structure. One possible order of visiting the nodes of the following graph is

(A) MNOPQR (B) NQMPOR (C) QMNPRO (D) QMNPOR

20. The data blocks of a very large file in the Unix file system are allocated using

(A) contiguous allocation

(B) linked allocation

(C) indexed allocation

(D) an extension of indexed allocation


21. The minimum number of equal length subintervals needed to approximate 2

x 6

1

1xe dx to an accuracy of at least 10 using the trapezoidal rule is

3

−×∫

(A) 1000e (B) 1000 (C) 100e (D) 100

22. The Newton-Raphson iteration n 1 n

n

1 Rx x

2 x+

= +

can be used to compute the

(A) square of R (B) reciprocal of R

(C) square root of R (D) logarithm of R

23. Which of the following statements is true for every planar graph on n vertices?

(A) The graph is connected

(B) The graph is Eulerian

(C) The graph has a vertex-cover of size at most 3n/4

(D) The graph has an independent set of size at least n/3

24. 1 i 2k 1 i 2ki odd i even

Let P i and Q i, where k is a positive integer. Then≤ ≤ ≤ ≤

= =∑ ∑

(A) P Q K= − (B) P Q K= + (C) P = Q (D) P Q 2K= +

M N O

R Q P




25. A point on a curve is said to be an extremum if it is a local minimum or a local

maximum. The number of distinct extrema for the curve 4 3 23x 16x 24x 37 is− + +

(A) 0 (B) 1 (C) 2 (D) 3

26. If P, Q, R are Boolean variables, then

( ) ( ) ( )P Q P.Q P.R P.R Q+ + +

Simplifies to

(A) P.Q (B) P.R (C) P.Q R+ (D) P.R Q+

27. Aishwarya studies either computer science or mathematics everyday. If she

studies computer science on a day, then the probability that the studies

mathematics the next day is 0.6. If she studies mathematics on a day, then the

probability that the studies computer science the next day is 0.4. Given that

Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

(A) 0.24 (B) 0.36 (C) 0.4 (D) 0.6

28. How many of the following matrices have an eigenvalue 1?

1 0 0 1 1 1 1 0

and0 0 0 0 1 1 1 1

− − −

(A) one (B) two (C) three (D) four

29. Let X be a random variable following normal distribution with mean +1 and

variance 4. Let Y be another normal variable with mean -1 and variance

unknown. If ( ) ( )P X 1 P Y 2 ,≤ − = ≥ the standard deviation of Y is

(A) 3 (B) 2 (C) 2 (D) 1

30. Let fsa and pda be two predicates such that fsa(x) means x is a finite state

automaton, and pda(y) means that y is a pushdown automaton. Let equivalent

be another predicate such that equivalent (a, b) means a and b are equivalent.

Which of the following first order logic statements represents the following:

Each finite state automaton has an equivalent pushdown automaton

(A) ( )( ) ( ) ( )( )x fsa x y pda y equivalent x,y∀ ⇒ ∃ ∧

(B) ( ) ( ) ( )( )~ y x fsa x pda y equivalent x,y∀ ∃ ⇒ ∧

(C) ( ) ( ) ( )( )x y fsa x pda y equivalent x,y∀ ∃ ∧ ∧

(D) ( ) ( ) ( )( )x y fsa y pda x equivalent x,y∀ ∃ ∧ ∧




31. P and Q are two propositions. Which of the following logical expressions are

equivalent?

( )

( ) ( ) ( )( ) ( ) ( )

I. P ~ Q

II. ~ ~ P Q

III. P Q P ~ Q ~ P ~ Q

IV. P Q P ~ Q ~ P Q

∨

∧

∧ ∨ ∧ ∨ ∧

∧ ∨ ∧ ∨ ∧

(A) Only I and II (B) Only I, II and III

(C) Only I, II and IV (D) All of I, II III and IV

32. For a magnetic disk with concentric circular tracks, the seek latency is not linearly

proportional to the seek distance due to

(A) non-uniform distribution of requests

(B) arm starting and stopping inertia

(C) higher capacity of tracks on the periphery of the platter

(D) use of unfair arm scheduling policies

33. Which of the following is/are true of the auto-increment addressing mode?

I. It is useful in creating self-relocating code

II. If it is included in an Instruction Set Architecture, then an additional ALU is

required for effective address calculation

III. The amount of increment depends on the size of the data item accessed

(A) I only (B) II only (C) III only (D) II and III only

34. Which of the following must be true for the RFE (Return From Exception)

instruction on a general purpose processor?

I. It must be a trap instruction

II. It must be a privileged instruction

III. An exception cannot be allowed to occur during execution of an RFE

instruction


(C) I and II only (D) I, II and III only

35. For inclusion to hold between two cache levels L1 and L2 in a multi-level cache

hierarchy, which of the following are necessary?

I. L1 must be a write-through cache

II. L2 must be a write-through cache

III. The associativity of L2 must be greater than that of L1

IV. The L2 cache must be at least as large as the L1 cache

(A) IV only (B) I and IV only

(C) I, II and IV only (D) I, II, III and IV




36. Which of the following are NOT true in a pipelined processor?

I. Bypassing can handle all RAW hazards

II. Register renaming can eliminate all register carried WAR hazards

III. Control hazard penalties can be eliminated by dynamic branch prediction

(A) I and II only (B) I and III only (C) II and III only (D) I, II and III

37. The use of multiple register windows with overlap causes a reduction in the

number of memory accesses for

I. Function locals and parameters

II. Register saves and restores

III. Instruction fetches

(A) I only (B) II only (C) III only (D) I, II and III

38. In an instruction execution pipeline, the earliest that the data TLB (Translation

Lookaside Buffer) can be accessed is

(A) Before effective address calculation has started

(B) During effective address calculation

(C) After effective address calculation has completed

(D) After data cache lookup has completed

39. Consider the following functions:

( )( )( )

n

logn

f n 2

g n n!

h n n

=

=

=

Which of the following statements about the asymptotic behaviour of f(n), g(n),

and h(n) is true?

(A) ( ) ( )( ) ( ) ( )( )f n O g n ; g n O h n= = (B) ( ) ( )( ) ( ) ( )( )f n g n ; g n O h n= Ω =

(C) ( ) ( )( ) ( ) ( )( )g n O f n ; h n O f n= = (D) ( ) ( )( ) ( ) ( )( )h n O f n ; g n f n= = Ω

40. The minimum number of comparisons required to determine if an integer appears

more than n/2 times in a sorted array of n integers is

(A) ( )nΘ (B) ( )lognΘ (C) ( )log*nΘ (D) ( )1Θ

41. A B-tree of order 4 is built from scratch by 10 successive insertions. What is the

maximum number of node splitting operations that may take place?

(A) 3 (B) 4 (C) 5 (D) 6

42. G is a graph on n vertices and 2n-2 edges. The edges of G can be partitioned into

two edge-disjoint spanning trees. Which of the following is NOT true for G?

(A) For every subset of k vertices, the induced subgraph has at most 2k-2 edges




(B) The minimum cut in G has at least two edges

(C) There are two edge-disjoint paths between every pair of vertices

(D) There are two vertex-disjoint paths between every pair of vertices

43. Consider the Quicksort algorithm. Suppose there is a procedure for finding a

pivot element which splits the list into two sub-lists each of which contains at

least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Then

(A) ( ) ( )T n 2T n /5 n≤ + (B) ( ) ( ) ( )T n T n /5 T 4n /5 n≤ + +

(C) ( ) ( )T n 2T 4n /5 n≤ + (D) ( ) ( )T n 2T n /2 n≤ +

44. The subset-sum problem is defined as follows: Given a set S of n positive

integers and a positive integer W, determine whether there is a subset of S Whose elements sum to W.

An algorithm Q solves this problem in O(nW) time. Which of the following

statements is false?

(A) Q solves the subset-sum problem in polynomial time when the input is

encoded in unary

(B) Q solves the subset-sum problem in polynomial time when the input is

encoded in binary

(C) The subset sum problem belongs to the class NP

(D) The subset sum problem is NP-hard

45.

Dijkstra’s single source shortest path algorithm when run from vertex a in the

above graph, computes the correct shortest path distance to

(A) only vertex a (B) only vertices a, e, f, g, h

(C) only vertices a, b, c, d (D) all the vertices

46. You are given the postorder traversal, P, of a binary search tree on the n

elements 1, 2,….,n. You have to determine the unique binary search tree that has

P as its postorder traversal. What is the time complexity of the most efficient algorithm for doing this?

(A) ( )lognΘ (B) ( )nΘ (C) ( )nlognΘ

(D) None of the above, as the tree cannot be uniquely determined

b

a c

d

2

1 2

3

e

h f

g

2

1 2

3

1

5−

3−

2




47. We have a binary heap on n elements and wish to insert n more elements (not

necessarily one after another) into this heap. The total time required for this is

(A) ( )lognΘ (B) ( )nΘ (C) ( )nlognΘ (D) ( )2nΘ

48. Which of the following statements is false?

(A) Every NFA can be converted to an equivalent DFA

(B) Every non-deterministic Turing machine can be converted to an equivalent

deterministic Turing machine

(C) Every regular language is also a context-free language

(D) Every subset of a recursively enumerable set is recursive

49. Given below are two finite state automata (→ indicates the start state and F

indicates a final state)

Y:

( )

a b

1 1 2

2 F 2 1

→ Z:

( )

a b

1 2 2

2 F 1 1

→

Which of the following represents the product automaton Z×Y?

(A)

( )

a b

P S R

Q R S

R F Q P

S Q P

→ (B)

( )

a b

P S Q

Q R S

R F Q P

S P Q

→ (C)

( )

a b

P Q S

Q R S

R F Q P

S Q P

→ (D)

( )

a b

P S Q

Q S R

R F Q P

S Q P

→

50. Which of the following statements are true?

I. Every left-recursive grammar can be converted to a right-recursive grammar

and vice-versa

II. All ε-productions can be removed from any context-free grammar by suitable

transformations

III. The language generated by a context-free grammar all of whose productions are of the form X w or X wY→ → (where, w is a string of terminals and Y is

a non-terminal), is always regular

IV. The derivation trees of strings generated by a context-free grammar in

Chomsky Normal Form are always binary trees

(A) I,II,III and IV (B) II,III and IV only

(C) I,III and IV only (D) I,II and IV only




51. Match the following:

E. Checking that identifiers are

declared before their use

P. n m n mL a b c d n 1,m 1= ≥ ≥

F. Number of formal parameters in

the declaration of a function

agrees with the number of actual parameters in use of that function

Q. X XbX XcX dXf g→

G. Arithmetic expressions with

matched pairs of parentheses

R. L wcw w (a b)*= ∈

H. Palindromes S. X bXb cXc→ ε

(A) E P, F R, G Q, H S− − − − (B) E R, F P, G S, H Q− − − −

(C) E R, F P, G Q, H S− − − − (D) E P, F R, G S, H Q− − − −

52. Match the following NFAs with the regular expressions they correspond to

P.

Q.

R.

S.

1. ( )0 01*1 00 *01*ε + +

2. ( )0 10 *1 00 * 0ε + +

3. ( )0 10 *1 10 *1ε + +

4. ( )0 10 *1 10 *10 *ε + +

10

0

0

1

01

0

0

1

01

1

0

1

01

10

1




(A) P 2, Q 1, R 3, S 4− − − − (B) P 1, Q 3, R 2, S 4− − − −

(C) P 1, Q 2, R 3, S 4− − − − (D) P 3, Q 2, R 1, S 4− − − −

53. Which of the following are regular sets?

I. n 2ma b n 0,m 0≥ ≥

II. n ma b n 2m=

III. n ma b n m≠

IV. xcy x,y, a,b *∈

(A) I and IV only (B) I and III only (C) I only (D) IV only

54. Which of the following are true?

I. A programming language which does not permit global variables of any kind

and has no nesting of procedures/functions, but permits recursion can be

implemented with static storage allocation

II. Multi-level access link (or display) arrangement is needed to arrange

activation records only if the programming language being implemented has

nesting of procedures/functions

III. Recursion in programming languages cannot be implemented with dynamic

storage allocation

IV. Nesting procedures/functions and recursion require a dynamic heap

allocation scheme and cannot be implemented with a stack-based allocation

scheme for activation records

V. Programming languages which permit a function to return a function as its

result cannot be implemented with a stack-based storage allocation scheme for activation records

(A) II and V only (B) I, III and IV only

(C) I, II and V only (D) II, III and V only

55. An LALR(1) parser for a grammar G can have shift-reduce (S-R) conflicts if and

only if

(A) The SLR(1) parser for G has S-R conflicts

(B) The LR(1) parser for G has S-R conflicts

(C) The LR(0) parser for G has S-R conflicts

(D) The LALR(1) parser for G has reduce-reduce conflicts

56. In the slow start phase of the TCP congestion control algorithm, the size of the

congestion window

(A) does not increase (B) increases linearly

(C) increases quadratically (D) increases exponentially




57. If a class B network on the Internet has a subnet mask of 255.255.248.0, what is

the maximum number of hosts per subnet?

(A) 1022 (B) 1023 (C) 2046 (D) 2047

58. A computer on a 10Mbps network is regulated by a token bucket. The token

bucket is filled at a rate of 2Mbps. It is initially filled to capacity with 16Megabits.

What is the maximum duration for which the computer can transmit at the full 10Mbps?

(A) 1.6 seconds (B) 2 seconds (C) 5 seconds (D) 8 seconds

59. A client process P needs to make a TCP connection to a server process S.

Consider the following situation: the server process S executes a socket (), a

bind () and a listen () system call in that order, following which it is preempted.

Subsequently, the client process P executes a socket () system call followed by

connect () system call to connect to the server process S. The server process has

not executed any accept () system call. Which one of the following events could take place?

(A) connect () system call returns successfully

(B) connect () system call blocks

(C) connect () system call returns an error

(D) connect () system call results in a core dump

60. What is printed by the following C program?

( ) ( )

( )( )

int f int x, int *py, int **ppz void main

int y, z; int c, *b, **a;**ppz 1; z *ppz; c 4; b &c; a &b;

*py 2; y *py; pr int f "%d", f c,b,a ;

x 3; return x y z;

+ = = = = =+ = =

+ =+ +

(A) 18 (B) 19 (C) 21 (D) 22

61. Choose the correct option to fill ? 1 and ? 2 so that the program below prints an

input string in reverse order. Assume that the input string is terminated by a newline character.

( )

( ) ( )

( )( ) ( )

( ) ( )

void recerse void

int c;

if ?1 reverse ;

?2

main

pr int f "Enter Text " ; pr int f "\ n" ;

reverse ;pr int f "\ n" ;




(A) ( )( )?1 is getchar ! '\ n'=

( )?2 is getchar c ;

(B) ( ) )( )?1 is c getchar ! '\ n'= =

( )?2 is getchar c ;

(C) ( )?1 is c ! '\ n'=

( )?2 is putchar c ;

(D) ( ( ) )( )?1 is c getchar ! '\ n'= =

( )?2 is putchar c ;

62. The following C function takes a single-linked list of integers as a parameter and

rearranges the elements of the list. The function is called with the list containing

the integers 1,2,3,4,5,6,7 in the given order. What will be the contents of the list after the function completes execution?

( )

( )

( )

struct node

int value;

struct node *next;

;

Void rearrange struct node * list

struct node *p, * q;

int temp;

if !list !list next return;

p list; q list next;

while q

temp p value;p value q value;

q value temp;p q next;

q

− >

= = − >

= − > − > = − >− > = = − >

p?p next : 0;

= − >

(A) 1,2,3,4,5,6,7 (B) 2,1,4,3,6,5,7 (C) 1,3,2,5,4,7,6 (D) 2,3,4,5,6,7,1

63. The P and V operations on counting semaphores, where s is a counting

semaphore, are defined as follows:

( )

( )

P s : s s 1;

ifs 0 then wait;

V s : s s 1;

ifs 0 then wakeup a process waiting on s;

= −

<

= +

<=

Assume that Pb and Vb the wait and signal operations on binary semaphores are

provided. Two binary semaphores xb and yb are used to implement the semaphore operations P(s) and V(s) as follows:




( ) ( )

( )( )( )

( )

( ) ( )

( ) ( )( )

b b

b b

b b

b b

b b

b b

b b

P s : P x ;

s s 1;

if s 0

V x ;

P y ;

else V x ;

V s : P x ;

s s 1;

if s 0 V y ;

V x ;

= −

<

= +

<=

The initial values of xb and yb are respectively

(A) 0 and 0 (B) 0 and 1 (C) 1 and 0 (D) 1 and 1

64. Which of the following statements about synchronous and asynchronous I/O is

NOT true?

(A) An ISR is invoked on completion of I/O in synchronous I/O but not in

asynchronous I/O

(B) In both synchronous and asynchronous I/O, an ISR (Interrupt Service

Routine) is invoked after completion of the I/O

(C) A process making a synchronous I/O call waits until I/O is complete, but a

process making an asynchronous I/O call does not wait for completion of the

I/O

(D) In the case of synchronous I/O, the process waiting for the completion of I/O

is woken up by the ISR that is invoked after the completion of I/O

65. Which of the following is NOT true of deadlock prevention and deadlock

avoidance schemes?

(A) In deadlock prevention, the request for resources is always granted if the

resulting state is safe

(B) In deadlock avoidance, the request for resources is always granted if the

result state is safe

(C) Deadlock avoidance is less restrictive than deadlock prevention

(D) Deadlock avoidance requires knowledge of resource requirements a priori

66. A process executes the following code

( ) ( )for i 0; i n; i for ;= < + +

The total number of child processes created is

(A) n (B) n2 1− (C) n2 (D) n 12 1+ −




67. A processor uses 36 bit physical addresses and 32 bit virtual addresses, with a

page frame size of 4 Kbytes. Each page table entry is of size 4 bytes. A three

level page table is used for virtual to physical address translation, where the virtual address is used as follows

• Bits 30-31 are used to index into the first level page table

• Bits 21-29 are used to index into the second level page table

• Bits 12-20 are used to index into the third level page table, and

• Bits 0-11 are used as offset within the page

The number of bits required for addressing the next level page table (or page

frame) in the page table entry of the first, second and third level page tables are respectively

(A) 20, 20 and 20 (B) 24, 24 and 24 (C) 24, 24 and 20 (D) 25, 25 and 24

68. Let R and S be two relations with the following schema

( )( )

R P,Q,R1,R2,R3

S P,Q,S1,S2

Where P, Q is the key for both schemas. Which of the following queries are equivalent?

( )( ) ( )

( ) ( )( )( ) ( ) ( )( )( )

P

P P

P P,Q P,Q

P P,Q P,Q P,Q

I. R S

II. R S

III. R S

IV. R R S

Π

Π Π

Π Π ∩ Π

Π Π − Π − Π

(A) Only I and II (B) Only I and III

(C) Only I, II and III (D) Only I, III and IV

69. Consider the following relational schemes for a library database:

( )

( )Book Title,Author,Catalog_no, Publisher, Year, Pr ice

Collection Title,Author,Catalog_no

with in the following functional dependencies:

I. Title Author Catalog_no

II. Catalog_no Title Author Publisher Year

III. Publisher Title Year Pr ice

→

→

→

Assume Author, Title is the key for both schemes. Which of the following

statements is true?

(A) Both Book and Collection are in BCNF

(B) Both Book and Collection are in 3NF only

(C) Book is in 2NF and Collection is in 3NF

(D) Both Book and Collection are in 2NF only




70. Consider a file of 16384 records. Each record is 32 bytes long and its key field is

of size 6 bytes. The file is ordered on a non-key field, and the file organization is

unspanned. The file is stored in a file system with block size 1024 bytes, and the

size of a block pointer is 10 bytes. If the secondary index is built on the key field

of the file, and a multi-level index scheme is used to store the secondary index,

the number of first-level and second-level blocks in the multi-level index are

respectively


Common Data for Questions: 71 72 and 73

Consider a machine with a 2-way set associative data cache of size 64Kbytes and

block size 16bytes. The cache is managed using 32 bit virtual addresses and the page size is 4Kbyts. A program to be run on this machine begins as follows:

( )

( )

double ARR 1024 1024 ;

int i, j ;

/* Initialize array ARR to 0.0 * /

for i 0;i 1024; i

for j 0; j 1024; j

ARR i j 0.0;

= < + +

= < + +

=

The size of double is 8Bytes. Array ARR is located in memory starting at the

beginning of virtual page 0xFF000 and stored in row major order. The cache is

initially empty and no pre-fetching is done. The only data memory references made by the program are those to array ARR

71. The total size of the tags in the cache directory is

(A) 32Kbits (B) 34Kbits (C) 64Kbits (D) 68Kbits

72. Which of the following array elements has the same cache index as ARR [0] [0]?

(A) ARR [0] [4] (B) ARR [4] [0] (C) ARR [0] [5] (D) ARR [5] [0]

73. The cache hit ratio for this initialization loop is

(A) 0% (B) 25% (C) 50% (D) 75%




Common Data for Questions: 74 and 75

Consider the following C functions:

( )

( )

( ) ( )( )

( )

( )

int f1 int n

if n 0 n 1

return n;

else

return 2 * f1 n 1 3* f1 n 2 ;

int f2 int n

int i;

int X N , Y N , Z N ;

X 0 Y 0 Z 0 0;

X 1 1; Y 1 2; Z 1 3;

for i 2; i n; i

X i Y i 1 Z i 2 ;

Y i 2 * X i

= = = =

− + −

= = =

= = =

= <= + +

= − + −

= ;

Z i 3 * X i ;

return X n ;

=

74. The running time of f1 (n) and f2 (n) are

(A) ( ) ( )n and nΘ Θ (B) ( ) ( )n2 and nΘ Θ

(C) ( ) ( )nn and 2Θ Θ (D) ( ) ( )n n2 and 2Θ Θ

75. F1 (8) and f2 (8) return the values

(A) 1661 and 1640 (B) 59 and 59

(C) 1640 and 1640 (D) 1640 and 1661




Linked Answer Questions: Q.76 to 85 Carry Two Marks Each

Statement for Linked Answer Questions: 76 & 77

Delayed branching can help in the handling of control hazards

76. For all delayed conditional branch instructions, irrespective of whether the condition evaluates to true or false

(A) The instruction following the conditional branch instruction in memory is executed

(B) The first instruction in the fall through path is executed

(C) The first instruction in the taken path is executed

(D) The branch takes longer to execute than any other instruction

77. The following code is to run on a pipelined processor with one branch delay slot:

I1: ADD R2 R7 R8

I2 : SUB R4 R5 R6

I3 : ADD R1 R2 R3

I4 : STORE Memory R4 R1

BRANCH to Label if R1 0

← +

← −

← +

←

= =

Which of the instructions I1, I2, I3 or I4 can legitimately occupy the delay slot without any other program modification?

(A) I1 (B) I2 (C) I3 (D) I4


Let xn denote the number of binary strings of length n that contain no consecutive 0s.

78. Which of the following recurrences does xn satisfy?

(A) n n 1

x 2x −= (B) n n /2x x 1= + (C) n n /2x x n= + (D) n n 1 n 2

x x x− −= +

79. The value of x5 is

(A) 5 (B) 7 (C) 8 (D) 16


The subset-sum problem is defined as follows. Given a set of n positive integers,

1 2 3 nS a ,a ,a ,...,a ,= and positive integer W, is there a subset of S whose

elements sum to W? A dynamic program for solving this problem uses a

2-dimensional Boolean array, X, with n rows and W+1 columns.




X i, j ,1 i n,0 j W,≤ ≤ ≤ ≤ is TRUE if and only if there is a subset of 1 2 ia ,a ,...,a

whose elements sum to j.

80. Which of the following is valid for i

2 i n and a j W?≤ ≤ ≤ ≤

(A) iX i, j X i 1, j X i, j a= − ∨ − (B) iX i, j X i 1, j X i 1, j a= − ∨ − −

(C) iX i, j X i 1, j X i, j a= − ∧ − (D) iX i, j X i 1, j X i 1, j a= − ∧ − −

81. Which entry of the array X, if TRUE, implies that there is a subset whose

elements sum to W?

(A) X 1,W (B) X n,0 (C) X n,W (D) X n 1,n−


Consider the following ER diagram

82. The minimum number of tables needed to represent M, N, P, R1, R2 is

(A) 2 (B) 3 (C) 4 (D) 5

83. Which of the following is a correct attribute set for one of the tables for the

correct answer to the above question?

(A) M1,M2,M3,P1 (B) M1,P1,N1,N2 (C) M1,P1,N1 (D) M1,P1


Consider the following C program that attempts to locate an element x in an

array Y[ ] using binary search. The program is erroneous.

( )

( )( )

( ) ( )( )( ) ( )

( )

1. f int Y 10 , int x

2. int u, j, k;3. i 0; j 9;4. do

5. k i j / 2;

6. if Y k x i k;else j k;

7. while Y k ! x & & i j ;

8. if Y k x pr int f "x is in the array " ;

9. else pr int f " x is not in the array " ;

10.

= =

= +

< = =

= <

= =

M1 M2 M3

M P

N2N1P2P1

R1 R2 N




84. On which of the following contents of Y and x does the program fail?

(A) Y is 1 2 3 4 5 6 7 8 9 10 and x 10<

(B) Y is 1 3 5 7 9 11 13 15 17 19 and x 1<

(C) Y is 2 2 2 2 2 2 2 2 2 2 and x 2>

(D) Y is 2 4 6 8 10 12 14 16 18 20 and 2 x 20 and x is even< <

85. The correction needed in the program to make it work properly is

(A) ( )Change line 6 to:if Y k x i k 1; else j k 1;< = + = −

(B) ( )Change line 6 to:if Y k x i k 1; else j k 1;< = − = +

(C) ( )Change line 6 to:if Y k x i k; else j k;< = = =

(D) ( ) ( )( )Change line 7 to: while Y k x & & i j ;= = <




Q. No. 1 – 20 Carry One Mark Each

1. Which one of the following in NOT necessarily a property of a Group?

(A) Commutativity (B) Associativity

(C) Existence of inverse for every element (D) Existence of identity

2. What is the chromatic number of an n-vertex simple connected graph which does

not contain any odd length cycle? Assume n ≥2.

(A) 2 (B) 3 (C) n-1 (D) n

3. Which one of the following is TRUE for any simple connected undirected graph

with more than 2 vertices?

(A) No two vertices have the same degree.

(B) At least two vertices have the same degree.

(C) At least three vertices have the same degree.

(D) All vertices have the same degree.

4. Consider the binary relation R = (x,y), (x,z), (z,x), (z,y) on the set x,y,z.


(A) R is symmetric but NOT antisymmetric

(B) R is NOT symmetric but antisymmetric

(C) R is both symmetric and antisymmetric

(D) R is neither symmetric nor antisymmetric

5. (1217)8 is equivalent to

(A) (1217)16 (B) (028F)16 (C) (2297)10 (D) (0B17)16

6. What is the minimum number of gates required to implement the Boolean

function (AB+C) if we have to use only 2-input NOR gates?

(A) 2 (B) 3 (C) 4 (D) 5

7. How many 32K x 1 RAM chips are needed to provide a memory capacity of 256K-

bytes?

(A) 8 (B) 32 (C) 64 (D) 128

8. A CPU generally handles an interrupt by executing an interrupt service routine

(A) As soon as an interrupt is raised

(B) By checking the interrupt register at the end of fetch cycle.

(C) By checking the interrupt register after finishing the execution of the current

instruction.

(D) By checking the interrupt register at fixed time intervals.




9. In which one of the following page replacement policies, Belady’s anomaly may occur?

(A) FIFO (B) Optimal (C) LRU (D) MRU

10. The essential content(s) in each entry of a page table is / are

(A) Virtual page number

(B) Page frame number

(C) Both virtual page number and page frame number

(D) Access right information

11. What is the number of swaps required to sort n elements using selection sort, in

the worst case?

(A) (n)θ (B) (n log n)θ (C) 2(n )θ (D) 2(n log n)θ

12. S aSa bSb a b→ ;The language generated by the above grammar over the

alphabet a,b is the set of

(A) All palindromes.

(B) All odd length palindromes.

(C) Strings that begin and end with the same symbol

(D) All even length palindromes.

13. Which of the following statement(s) is / are correct regarding Bellman-Ford

shortest path algorithm?

P. Always finds a negative weighted cycle, if one exists.

Q. Finds whether any negative weighted cycle is reachable from the source.

(A) P only (B) Q only

(C) both P and Q (D) Neither P nor Q

14. Let Aπ be a problem that belongs to the class NP. Then which one of the

following is TRUE?

(A) There is no polynomial time algorithm for Aπ .

(B) If Aπ can be solved deterministically in polynomial time, then P = NP.

(C) If Aπ is NP-hard, then it is NP-complete.

(D) Aπ may be undecidable.

15. Which one of the following languages over the alphabet 0,1 is described by the

regular expression: (0+1)*0(0+1)*0(0+1)*?

(A) The set of all strings containing the substring 00.

(B) The set of all strings containing at most two 0’s.

(C) The set of all strings containing at least two 0’s.

(D) The set of all strings that begin and end with either 0 or 1.




16. Which one of the following is FALSE?

(A) There is unique minimal DFA for every regular language

(B) Every NFA can be converted to an equivalent PDA.

(C) Complement of every context-free language is recursive.

(D) Every nondeterministic PDA can be converted to an equivalent deterministic

PDA.

17. Match all items in Group 1 with correct options from those given in Group 2.

Group 1 Group 2

P. Regular expression 1. Syntax analysis

Q. Pushdown automata 2. Code generation

R. Dataflow analysis 3. Lexical analysis

S. Register allocation 4. Code optimization

(A) P-4. Q-1, R-2, S-3 (B) P-3, Q-1, R-4, S-2

(C) P-3, Q-4, R-1, S-2 (D) P-2, Q-1, R-4, S-3

18. Consider the program below:

# include < stdio.h >int fun(int n, int * f_p)

int t, f;if (n <=1)

* f_p =1;return 1;

t = fun (n-1, f_p);f = t+*f_p;* f_p = t;return f;

int main()

int x = 15;printf ("%d\ n", fun(5,& x));return 0;

The value printed is

(A) 6 (B) 8 (C) 14 (D) 15

19. The coupling between different modules of a software is categorized as follows:

I. Content coupling II. Common coupling

III. Control coupling IV Stamp coupling

V. Data coupling

Coupling between modules can be ranked in the order of strongest (least desirable) to weakest (most desirable) as follows:

(A) I-II-III-IV-V (B) V-IV-III-II-I (C) I-III-V -II-IV (D) IV-II-V -III-I




20. Consider the HTML table definition given below:

table border=1><tr> <td rowspan=2> ab </td> <td colspan=2> cd </td></tr><tr> <td> ef </td> <td rowspan=2> gh </td></tr><tr> <td colspan=2> ik </td></tr>

</table>

<

The number of rows in each column and the number of columns in each row are:

(A) 2,2,3 and 2,3,2 (B) 2,2,3 and 2,2,3

(C) 2,3,2 and 2,3,2 (D) 2,3,2 and 2,2,3

Q. No. 21 – 56 Carry Two Marks Each

21. An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The

probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same.

If the probability that the face is even given that it is greater than 3 is 0.75,

which one of the following options is closest to the probability that the face value exceeds 3?

(A) 0.453 (B) 0.468 (C) 0.485 (D) 0.492

22. For the composition table of a cyclic group shown below

* a b c d

a a b c d

b b a d c

c c d b a

d d c a b

Which one of the following choices is correct?

(A) a, b are generators (B) b, c are generators

(C) c, d are generators (D) d, a are generators

23. Which one of the following is the most appropriate logical formula to represent

the statement? “Gold and silver ornaments are precious”.

The following notations are used:

G(x): x is a gold ornament

S(x): x is a silver ornament

P(x): x is precious

(A) ( ) ( ) ( )( )( )x P x G x S x∀ → ∧ (B) ( ) ( )( ) ( )( )x G x S x P x∀ ∧ →

(C) ( ) ( )( ) ( )( )x G x S x P x∃ ∧ → (D) ( ) ( )( ) ( )( )x G x S x P x∀ ∨ →




24. The binary operation is defined as follows

Which one of the following is equivalent to P Q∨ ?

(A) Q P¬ ¬ (B) P Q¬ (C) P Q¬ (D) P Q¬ ¬

25. ( ) ( )/ 4

0

1 tanx / 1 tanx dx

π

− +∫ evaluates to

(A) 0 (B) 1 (C) ln 2 (D) 1 ln 22

26. Consider the following well-formed formulae:

I. ( )( )x P x¬∀ II. ( )( )x P x¬∃ III. ( )( )x P x¬∃ ¬ IV. ( )( )x P x¬∃ ¬

Which of the above are equivalent?

(A) I and III (B) I and IV (C) II and III (D) II and IV

27. Given the following state table of an FSM with two states A and B, one input and one output:

Present

State A

Present

State B Input

Next

State A

Next

State B Output

0 0 0 0 0 1

0 1 0 1 0 0

1 0 0 0 1 0

1 1 0 1 0 0

0 0 1 0 1 0

0 1 1 0 0 1

1 0 1 0 1 1

1 1 1 0 0 1

If the initial state is A = 0, B=0, what is the minimum length of an input string

which will take the machine to the state A=0, B=1 with Output=1?

(A) 3 (B) 4 (C) 5 (D) 6

28. Consider a 4 stage pipeline processor. The number of cycles needed by the four

instructions I1, I2, I3, I4 in stages S1, S2, S3, S4 is shown below:

S1 S2 S3 S4

I1 2 1 1 1

I2 1 3 2 2

I3 2 1 1 3

I4 1 2 2 2

P Q PQ

T T T

T F T

F T F

F F T




What is the number of cycles needed to execute the following loop?

For (i=1 to 2) I1; I2; I3; I4;

(A) 16 (B) 23 (C) 28 (D) 30

29. Consider a 4-way set associative cache (initially empty) with total 16 cache

blocks. The main memory consists of 256 blocks and the request for memory

blocks is in the following order:

0, 255, 1, 4, 3, 8, 133, 159, 216, 129, 63, 8, 48, 32, 73, 92, 155.

Which one of the following memory block will NOT be in cache if LRU replacement policy is used?

(A) 3 (B) 8 (C) 129 (D) 216

30. Consider a system with 4 types of resources R1 (3 units), R2 (2 units), R3 (3

units), R4 (2 units). A non-preemptive resource allocation policy is used. At any

given instance, a request is not entertained if it cannot be completely satisfied.

Three processes P1, P2, P3 request the sources as follows if executed independently.

Process P1:

t=0: requests 2 units of R2

t=1: requests 1 unit of R3


t=5: releases 1 unit of R2

and 1 unit of R1.



t=10: Finishes

Process P2:





t=8: Finishes

Process P3:



t=5: releases 2 units of R1



t=9: Finishes

Which one of the following statements is TRUE if all three processes run concurrently starting at time t=0?

(A) All processes will finish without any deadlock

(B) Only P1 and P2 will be in deadlock.

(C) Only P1 and P3 will be in a deadlock.

(D) All three processes will be in deadlock.

31. Consider a disk system with 100 cylinders. The requests to access the cylinders

occur in following sequence:

4, 34, 10, 7, 19, 73, 2, 15, 6, 20

Assuming that the head is currently at cylinder 50, what is the time taken to

satisfy all requests if it takes 1ms to move from one cylinder to adjacent one and shortest seek time first policy is used?

(A) 95ms (B) 119ms (C) 233ms (D) 276ms




32. In the following process state transition diagram for a uniprocessor system, assume that there are always some processes in the ready state:

Now consider the following statements:

I. If a process makes a transition D, it would result in another process making

transition A immediately.

II. A process P2 in blocked state can make transition E while another process P1

is in running state.

III. The OS uses preemptive scheduling.

IV. The OS uses non-preemptive scheduling.

Which of the above statements are TRUE?

(A) I and II (B) I and III (C) II and III (D) II and IV

33. The enter_CS() and leave_CS() functions to implement critical section of a

process are realized using test-and-set instruction as follows:

( )

void enter_CS(X)

while test-and-set(X) ;

void leave_CS(X)

X=0;

In the above solution, X is a memory location associated with the CS and is

initialized to 0. Now consider the following statements:

I. The above solution to CS problem is deadlock-free

II. The solution is starvation free.

III. The processes enter CS in FIFO order.

IV More than one process can enter CS at the same time.

Which of the above statements is TRUE?

(A) I only (B) I and II (C) II and III (D) IV only

Start Ready Running Terminated

Blocked

A

B

C

D

E F




34. A multilevel page table is preferred in comparison to a single level page table for translating virtual address to physical address because

(A) It reduces the memory access time to read or write a memory location.

(B) It helps to reduce the size of page table needed to implement the virtual

address space of a process.

(C) It is required by the translation lookaside buffer.

(D) It helps to reduce the number of page faults in page replacement algorithms.

35. The running time of an algorithm is represented by the following recurrence relation:

n n 3

nT cn otherwise

3

T(n) =

≤

+

Which one of the following represents the time complexity of the algorithm?


36. The keys 12, 18, 13, 2, 3, 23, 5 and 15 are inserted into an initially empty hash

table of length 10 using open addressing with hash function h(k) = k mod 10 and

linear probing. What is the resultant hash table?

(A) (B) (C) (D)

37. What is the maximum height of any AVL-tree with 7 nodes? Assume that the

height of a tree with a single node is 0.

(A) 2 (B) 3 (C) 4 (D) 5

38. Consider the following graph:

c

a

b

d

e

f

g

3

5

4

2

6

5

6

6

6

3

5

4

0

1

2 2

3 23

4

5 15

6

7

8 18

9

0

1

2 12

3 13

4

5 5

6

7

8 18

9

0

1

2 12

3 13

4 2

5 3

6 23

7 5

8 18

9 15

0

1

2 12,2

3 13,3,23

4

5 5,15

6

7

8 18

9




Which one of the following is NOT the sequence of edges added to the minimum

spanning tree using Kruskal’s algorithm?

(A) (b,e) (e,f) (a,c) (b,c) (f,g) (c,d) (B) (b,e) (e,f) (a,c) (f,g) (b,c) (c,d)

(C) (b,e) (a,c) (e,f) (b,c) (f,g) (c,d) (D) (b,e) (e,f) (b,c) (a,c) (f,g) (c,d)

39. In quick sort, for sorting n elements, the (n/4)th smallest element is selected as

pivot using an O(n) time algorithm. What is the worst case time complexity of the quick sort?


40. Let 1 2L L L= I , where L1 and L2 are languages as defined below:

m m n m1

i j k2

L a b c a b |m,n 0

L ab c | i, j,k 0

= ≥

= ≥

Then L is

(A) Not recursive

(B) Regular

(C) Context free but not regular

(D) Recursively enumerable but not context free.

41.

The above DFA accepts the set of all strings over 0,1 that

(A) begin either with 0 or 1 (B) end with 0

(C) end with 00 (D) contain the substring 00.

42. Which of the following statements are TRUE?

I There exist parsing algorithms for some programming languages whose

complexities are less than ( )3nθ .

II A programming language which allows recursion can be implemented with

static storage allocation.

III No L-attributed definition can be evaluated in the framework of bottom-up

parsing.

IV Code improving transformations can be performed at both source language

and intermediate code level.

(A) I and II (B) I and IV (C) III and IV (D) I, III and IV

1

0 0

0

1

1




43. Consider two transactions T1 and T2, and four schedules S1, S2, S3, S4 of T1 and T2

as given below:

1 1 1 1

2 2 2 2

1 1 2 2 1 1 2

2 1 2 2 1 2 1

3 1 1 2 1 2 2

4 2 2

T :R x W x W y

T :R x R y W y

S :R x R x R y W x W y W y

S :R x R x R y W x W y W y

S :R x W x R x W y R y W y

S :R x R y

1 1 1 2R x W x W y W y

Which of the above schedules are conflict-serializable?

(A) S1 and S2 (B) S2 and S3 (C) S3 only (D) S4 only

44. The following key values are inserted into a B+ - tree in which order of the

internal nodes is 3, and that of the leaf nodes is 2, in the sequence given below.

The order of internal nodes is the maximum number of tree pointers in each

node, and the order of leaf nodes is the maximum number of data items that can be stored in it. The B+ - tree is initially empty.

10, 3, 6, 8, 4, 2, 1

The maximum number of times leaf nodes would get split up as a result of these

insertions is

(A) 2 (B) 3 (C) 4 (D) 5

45. Let R and S be relational schemes such that R=a,b,c and S=c. Now consider the following queries on the database:

I. ( ) ( ) ( )( )R S R S R S R S,Sr r s r− − − −π − π π × − π

II. ( ) ( )( ) R St | t r u s v r u v s t v R S−∈ π ∧ ∀ ∈ ∃ ∈ = ∧ = −

III. ( ) ( )( ) R St | t r v r u s u v s t v R S−∈ π ∧ ∀ ∈ ∃ ∈ = ∧ = −

IV Select R.a, R.b

From R,S

Where R.c=S.c

Which of the above queries are equivalent?

(A) I and II (B) I and III (C) II and IV (D) III and IV

46. In the RSA public key cryptosystem, the private and public keys are (e,n) and

(d,n) respectively, where n=p*q and p and q are large primes. Besides, n is

public and p and q are private. Let M be an integer such that 0<M<n and

( ) ( ) ( )n p 1 q 1 .φ = − − Now consider the following equations.

I

( )' e

d'

M M mod n

M = M mod n

= II. ed 1mod n≡

III. ( )ed 1mod n≡ φ IV.

( )' e

d'

M M mod (n)

M = M mod (n)

= φ

φ




Which of the above equations correctly represent RSA cryptosystem?

(A) I and II (B) I and III (C) II and IV (D) III and IV

47. While opening a TCP connection, the initial sequence number is to be derived

using a time-of-day (ToD) clock that keeps running even when the host is down.

The low order 32 bits of the counter of the ToD clock is to be used for the initial

sequence numbers. The clock counter increments once per millisecond. The maximum packet lifetime is given to be 64s.

Which one of the choices given below is closest to the minimum permissible rate at which sequence numbers used for packets of a connection can increase?

(A) 0.015/s (B) 0.064/s (C) 0.135/s (D) 0.327/s

48. Let G(x) be the generator polynomial used for CRC checking. What is the condition that should be satisfied by G(x) to detect odd number of bits in error?

(A) G(x) contains more than two terms

(B) G(x) does not divide 1+xk, for any k not exceeding the frame length

(C) 1+x is a factor of G(x)

(D) G(x) has an odd number of terms.


I The context diagram should depict the system as a single bubble.

II External entities should be identified clearly at all levels of DFDs.

III Control information should not be represented in a DFD.

IV A data store can be connected either to another data store or to an external entity.

(A) II and III (B) II and III (C) I and III (D) I, II and III

50. Consider the following statements about the cyclomatic complexity of the control flow graph of a program module. Which of these are TRUE?

I. The cyclomatic complexity of a module is equal to the maximum number of linearly independent circuits in the graph.

II. The cyclomatic complexity of a module is the number of decisions in the

module plus one, where a decision is effectively any conditional statement in the module.

III. The cyclomatic complexity can also be used as a number of linearly independent paths that should be tested during path coverage testing.

(A) I and II (B) II and III (C) I and III (D) I, II and III

Common Data Questions: 51 & 52

A hard disk has 63 sectors per track, 10 platters each with 2 recording surfaces

and 1000 cylinders. The address of a sector is given as a triple c,h,s , where c

is the cylinder number, h is the surface number and s is the sector number. Thus,

the 0th sector is addressed as 0,0,0 , the 1st sector as 0,0,1 , and so on

51. The address <400, 16, 29> corre4sponds tp sector number:

(A) 505035 (B) 505036 (C) 505037 (D) 505038

52. The address of the 1039th sector is




(A) 0,15,31 (B) 0,16,30 (C) 0,16,31 (D) 0,17,31


A sub-sequence of a given sequence is just the given sequence with some

elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n, respectively, with indexes of X and Y starting from 0.

53. We wish to find the length of the longest common sub-sequence (LCS) of X[m]

and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of the LCS of X[m] and Y[n] is given below:

( )l i, j 0, if either i=0 or j=0

= expr1, if i,j>0 and X i-1 Y j 1

= expr2, if i,j>0 and X i-1 Y j 1

== − = −

Which one of the following options is correct?

(A) ( )expr1 l i 1, j 1≡ − + (B) ( )expr1 l i, j 1≡ −

(C) ( ) ( )( )expr2 max l i 1, j , l i,j-1≡ − (D) ( ) ( )( )expr2 max l i 1, j 1 , l i,j≡ − −

54. The values of l(i,j) could be obtained by dynamic programming based on the

correct recursive definition of l(i,j) of the form given above, using an array L[M,N], where M = m+1 and N=n+1, such that L[i,j] = l(i,j).

Which one of the following statements would be TRUE regarding the dynamic

programming solution for the recursive definition of l(i,j)?

(A) All elements L should be initialized to 0 for the values of l(i,j) to be properly

computed.

(B) The values of l(i,j) may be computed in a row major order or column major

order of L(M,N).

(C) The values of l(i,j) cannot be computed in either row major order or column

major order of L(M,N).

(D) L[p,q] needs to be computed before L[r,s] if either p<r or q<s.


Consider the following relational schema:

Suppliers(sid:integer, sname:string, city:string, street:string)Parts(pid:integer, pname:string, color:string) Catalog(sid:integer, pid:integer, cost:real)

55. Consider the following relational query on the above database:

SELECT S.snameFROM Suppliers SWHERE S.sid NOT IN (SELECT C.sid

FROM Catalog CWHERE C.pid NOT (SELECT P.pid

FROM Parts P WHERE P.color<> 'blue'))




Assume that relations corresponding to the above schema are not empty. Which one of the following is the correct interpretation of the above query?

(A) Find the names of all suppliers who have supplied a non-blue part.

(B) Find the names of all suppliers who have not supplied a non-blue part.

(C) Find the names of all suppliers who have supplied only blue parts.

(D) Find the names of all suppliers who have not supplied only blue parts.

56. Assume that, in the suppliers relation above, each supplier and each street within

a city has a unique name, and (sname, city) forms a candidate key. No other

functional dependencies are implied other than those implied by primary and

candidate keys. Which one of the following is TRUE about the above schema?

(A) The schema is in BCNF

(B) The schema is in 3NF but not in BCNF

(C) The schema is in 2NF but not in 3NF

(D) The schema is not in 2NF



Frames of 1000 bits are sent over a 106 bps duplex link between two hosts. The

propagation time is 25ms. Frames are to be transmitted into this link to

maximally pack them in transit (within the link).

57. What is the minimum number of bits (l) that will be required to represent the

sequence numbers distinctly? Assume that no time gap needs to be given between transmission of two frames.

(A) l=2 (B) l=3 (C) l=4 (D) l=5

58. Suppose that the sliding window protocol is used with the sender window size of

2l, where l is the number of bits identified in the earlier part and

acknowledgements are always piggy backed. After sending 2l frames, what is the

minimum time the sender will have to wait before starting transmission of the next frame? (Identify the closest choice ignoring the frame processing time.)

(A) 16ms (B) 18ms (C) 20ms (D) 22ms


Consider a binary max-heap implemented using an array.

59. Which one of the following array represents a binary max-heap?

(A) 25,12,16,13,10,8,14 (B) 25,14,13,16,10,8,12

(C) 25,14,16,13,10,8,12 (D) 25,14,12,13,10,8,16

60. What is the content of the array after two delete operations on the correct

answer to the previous question?

(A) 14,13,12,10,8 (B) 14,12,13,8,10

(C) 14,13,8,12,10 (D) 14,13,12,8,10

EX EX


© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the

written permission. Discuss this question paper at www.gatementor.com. 1


1. Let G=(V, E) be a graph. Define ( ) dd

ξ G i d= ×∑ , where id is the number of

vertices of degree d in G. If S and T are two different trees with ( ) ( )ξ = ξS T ,

then

(A) S 2 T= (B) S T 1= − (C) S T= (D) S T 1= +

2. Newton-Raphson method is used to compute a root of the equation 2x 13 0− =

with 3.5 as the initial value. The approximation after one iteration is

(A) 3.575 (B) 3.676 (C) 3.667 (D) 3.607

3. What is the possible number of reflexive relations on a set of 5 elements?

(A) 210 (B) 215 (C) 220 (D) 225

4. Consider the set S = 1, ω, ω2, where ω and ω2 are cube roots of unity. If *

denotes the multiplication operation, the structure (S, *) forms

(A) A group (B) A ring

(C) An integral domain (D) A field

5. What is the value of

2n

n

1lim 1 ?

n→∞

−

(A) 0 (B) e-2 (C) e-1/2 (D) 1

6. The minterm expansion of f (P, Q, R) PQ QR PR is= + +

(A) 2 4 6 7

m m m m+ + + (B) 0 1 3 5

m m m m+ + +

(C) 0 1 6 7

m m m m+ + + (D) 2 3 4 5

m m m m+ + +

7. A main memory unit with a capacity of 4 megabytes is built using 1M×1-bit

DRAM chips. Each DRAM chip has 1K rows of cells with 1K cells in each row. The

time taken for a single refresh operation is 100 nanoseconds. The time required

to perform one refresh operation on all the cells in the memory unit is

(A) 100 nanoseconds (B) 100*210 nanoseconds

(C) 100*220 nanoseconds (D) 3200*220 nanoseconds

8. P is a 16-bit signed integer. The 2’s complement representation of P is (F87B)16.

The 2’s complement representation of 8*P is

(A) ( )16

C3D8 (B) ( )16

187B (C) ( )16

F878 (D) ( )16

987B




9. The Boolean expression for the output f of the multiplexer shown below is

(A) P Q R⊕ ⊕

(B) P Q R⊕ ⊕

(C) P Q R+ +

(D) P Q R+ +

10. In a binary tree with n nodes, every node has an odd number of descendants.

Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child?

(A) 0 (B) 1 (C) ( )n 1 /2− (D) n-1

11. What does the following program print?

( )

( )

#include stdio.h

void f int *p, int * g

p q;

*p 2;

int i 0, j 1;

int main ( )

f(&i, & j);

pr int f "%d%d \ n", i, j ;

return 0;

< >

=

=

= =

(A) 2 2 (B) 2 1 (C) 0 1 (D) 0 2

12. Two alternative packages A and B are available for processing a database having

10k records. Package A requires 0.0001n2 time units and package B requires

10nlog10n time units to process n records. What is the smallest value of k for which package B will be preferred over A?

(A) 12 (B) 10 (C) 6 (D) 5

13. Which data structure in a compiler is used for managing information about variables and their attributes?

(A) Abstract syntax tree (B) Symbol table

(C) Semantic stack (D) Parse table

f

P Q

R

R

R

R




14. Which languages necessarily need heap allocation in the runtime environment?

(A) Those that support recursion (B) Those that use dynamic scoping

(C) Those that allow dynamic data structures (D) Those that use global variables

15. One of the header fields in an IP datagram is the Time to Live (TTL) field. Which

of the following statements best explains the need for this field?

(A) It can be used to prioritize packets

(B) It can be used to reduce delays

(C) It can be used to optimize throughput

(D) It can be used to prevent packet looping

16. Which one of the following is not a client server application?

(A) Internet chat (B) Web browsing (C) E-mail (D) Ping

17. Let L1 be a recursive language. Let L2 and L3 be languages that are recursively

enumerable but not recursive. Which of the following statements is not

necessarily true?

(A) L2 – L1 is recursively enumerable

(B) L1 – L3 is recursively enumerable

(C) L2 ∩ L1 is recursively enumerable

(D) L2 ∪ L1 is recursively enumerable

18. Consider a B+-tree in which the maximum number of keys in a node is 5. What is the minimum number of keys in any non-root node?

(A) 1 (B) 2 (C) 3 (D) 4

19. A relational schema for a train reservation database is given below

( )

( )Passenger pid, pname, age

Re servation pid, cass, tid

Table :Passenger

pid 'pname Age

0 'Sachin' 65

1 'Rahul' 66

2 'Sourav ' 67

3 'Anil ' 69

Table :Reservation

pid class tid

0 'AC ' 8200

1 'AC ' 8201

2 'SC ' 8201

5 'AC ' 8203

1 'SC ' 8204

3 'AC ' 8202




What pids are returned by the following SQL query for the above instance of the tables?

SELECT pid

FROM Reservation

WHERE class ' AC ' AND

EXISTS (SELECT *

FROM Passenger

WHERE age 65 AND

Passenger.pid Reservation.pid)

=

>

=

(A) 1, 0 (B) 1, 2 (C) 1, 3 (D) 1, 5

20. Which of the following concurrency control protocols ensure both conflict

serializability and freedom from deadlock?

I. 2-phase locking

II. Time-stamp ordering


(C) Both I and II (D) Neither I nor II

21. The cyclomatic complexity of each of the modules A and B shown below is

10. What is the cyclomatic complexity of the sequential integration shown on the right hand side?

(A) 19 (B) 21 (C) 20 (D) 10

22. What is the appropriate pairing of items in the two columns listing various activities encountered in a software life cycle?

P. Requirements Capture 1. Module Development and Integration

Q. Design 2. Domain Analysis

R. Implementation 3. Structural and Behavioral Modeling

S. Maintenance 4. Performance Tuning

(A) P-3, Q-2,R-4,S-1 (B) P-2, Q-3,R-1,S-4

(C) P-3, Q-2,R-1,S-4 (D) P-2, Q-3,R-4,S-1

A B

B

A




23. Consider the methods used by processes P1 and P2 for accessing their critical

sections whenever needed, as given below. The initial values of shared boolean

variables S1 and S2 are randomly assigned.

Method used by PI Method used by P2

while (S1 = = S2) ;

Critica1 Section

S1 = S2;

while (S1 != S2) ;

Critica1 Section

S2 = not (S1);

Which one of the following statements describes the properties achieved?

(A) Mutual exclusion but not progress

(B) Progress but not mutual exclusion

(C) Neither mutual exclusion nor progress

(D) Both mutual exclusion and progress

24. A system uses FIFO policy for page replacement. It has 4 page frames with no

pages loaded to begin with. The system first accesses 100 distinct pages in some

order and then accesses the same 100 pages but now in the reverse order. How

many page faults will occur?

(A) 196 (B) 192 (C) 197 (D) 195

25. Which of the following statements are true?

I. Shortest remaining time first scheduling may cause starvation

II. Preemptive scheduling may cause starvation

III. Round robin is better than FCFS in terms of response time

(A) I only (B) I and III only (C) II and III only (D) I, II and III


26. Consider a company that assembles computers. The probability of a faulty

assembly of any computer is p. The company therefore subjects each

computer to a testing process. This testing process gives the correct result for

any computer with a probability of q. What is the probability of a computer being declared faulty?

(A) ( ) ( )pq 1 p 1 q+ − − (B) ( )1 q p− (C) ( )1 p q− (D) pq

27. What is the probability that divisor of 1099 is a multiple of 1096?

(A) 1/625 (B) 4/625 (C) 12/625 (D) 16/625

28. The degree sequence of a simple graph is the sequence of the degrees of the

nodes in the graph in decreasing order. Which of the following sequences can not

be the degree sequence of any graph?

I. 7, 6, 5, 4, 4, 3, 2, 1 II. 6, 6, 6, 6, 3, 3, 2, 2




III. 7, 6, 6, 4, 4, 3, 2, 2 IV. 8, 7, 7, 6, 4, 2, 1, 1

(A) I and II (B) III and IV (C) IV only (D) II and IV

29. Consider the following matrix

2 3

Ax y

=

If the eigenvalues of A are 4 and 8, then

(A) x 4,y 10= = (B) x 5,y 8= = (C) x 3,y 9= − = (D) x 4,y 10= − =

30. Suppose the predicate F(x, y, t) is used to represent the statement that person x

can fool person y at time t. which one of the statements below expresses best

the meaning of the formula ( )x y t( F x,y, t )?∀ ∃ ∃ ¬

(A) Everyone can fool some person at some time

(B) No one can fool everyone all the time

(C) Everyone cannot fool some person all the time

(D) No one can fool some person at some time

31. What is the Boolean expression for the output f of the combinational logic circuit

of NOR gates given below?

(A) Q R+

(B) P Q+

(C) P R+

(D) P Q R+ +

32. In the sequential circuit shown below, if the initial value of the output Q1Q0 is 00, what are the next four values of Q1Q0?

(A) 11,10,01,00

(B) 10,11,01,00

(C) 10,00,01,11

(D) 11,10,00,01

T Q

1Q0Q

T Q1

Clock

PQ

QR

PR

QR

f




33. A 5-stage pipelined processor has Instruction Fetch (IF), Instruction Decode (ID),

Operand Fetch (OF), Perform Operation (PO) and Write Operand (WO) stages.

The IF, ID, OF and WO stages take 1 clock cycle each for any instruction. The PO

stage takes 1 clock cycle for ADD and SUB instructions, 3 clock cycles for MUL

instruction, and 6 clock cycles for DIV instruction respectively. Operand

forwarding is used in the pipeline. What is the number of clock cycles needed to

execute the following sequence of instructions?

0 2 0 1 2 0 1

1 5 3 4 5 3 4

2 2 5 2 2 5 2

3 5 2 6 5 2 6

Instruction Meaning of instruction

I :MUL R ,R ,R R R *R

I :DIV R ,R ,R R R /R

I : ADD R ,R ,R R R R

I : SUB R ,R ,R R R R

←←← +← −

(A) 13 (B) 15 (C) 17 (D) 19

34. The weight of a sequence a0, a1,…,an-1 of real numbers is defined as n 1

0 1 n 1a a /2 ... a /2 .−−+ + + A subsequence of a sequence is obtained by deleting

some elements from the sequence, keeping the order of the remaining elements

the same. Let X denote the maximum possible weight of a subsequence of

0 1 n 1a ,a ,...,a .− Then X is equal to

(A) ( )0max Y, a Y+ (B) ( )0max Y,a Y/2+ (C) ( )0

max Y, a 2Y+ (D) 0

a Y /2+

35. What is the value printed by the following C program?

#include stdio.h

int f(int * a, int n)

if (n 0)return 0;

else if(*a% 2 0) return * a f(a 1,n 1);

else return * a f(a 1, n 1);

int main ( )

int a[ ] 12, 7, 13, 4, 11, 6;

pr int f ("%d", f(a,6));

return 0;

< >

<=

= = + + −

− + −

=

(A) -9 (B) 5 (C) 15 (D) 19

36. The following C function takes a simply-linked list as input argument. It modifies

the list by moving the last element to the front of the list and returns the

modified list. Some part of the code is left blank.




typedef struct node

int value;

struct node *next;

Node;

Node *move_to_front(Node *head)

Node *p, *q;

if ((head = = NULL: || (head->next = = NULL)) return head;

q = NULL; p = head;

while (p-> next !=NULL)

q=P;

p=p->next;

_______________________________

return head;

Choose the correct alternative to replace the blank line.

(A) q = NULL; p->next = head; head = p;

(B) q->next = NULL; head = p; p->next = head;

(C) head = p; p->next = q; q->next = NULL;

(D) q->next = NULL; p->next = head; head = p;

37. The program below uses six temporary variables a, b, c, d, e, f.

a 1

b 10

c 20

d a b

e c d

f c e

b c e

e b f

d 5 e

return d f

=

=

=

= +

= +

= +

= +

= +

= +

+

Assuming that all operations take their operands from registers, what is the minimum number of registers needed to execute this program without spilling?

(A) 2 (B) 3 (C) 4 (D) 6

38. The grammar S aSa|bS|c is→

(A) LL(1) but not LR(1) (B) LR(1) but not LR(1)

(C) Both LL(1) and LR(1) (D) Neither LL(1) nor LR(1)




39. Let ( ) L w 0 1 *|w has even number of 1s ,= ∈ + i.e. L is the set of all bit strings

with even number of 1s. Which one of the regular expressions below represents

L?

(A) ( )0 *10 *1 * (B) ( )0 * 10 *10 * *

(C) ( )0 * 10 *1* * 0 * (D) ( )0 *1 10 *1 *10 *

40. Consider the languages i j i j i jL1 01 | i j . L2 01 | i j . L3 01 | i 2j 1 .= ≠ = = = = +

i jL4 01 | i 2j .= ≠ Which one of the following statements is true?

(A) Only L2 is context free (B) Only L2 and L3 are context free

(C) Only L1 and L2 are context free (D) All are context free

41. Let w be any string of length n in 0, 1*. Let L be the set of all substrings of w.

What is the minimum number of states in a non-deterministic finite automaton

that accepts L?

(A) n-1 (B) n (C) n+1 (D) 2n-1

42. Consider the following schedule for transactions T1, T2 and T3:

( )( )

( )( )

( )( )

( )( )

T1 T2 T3

Read X

Read Y

Read Y

Write Y

Write X

Write X

Read X

Write X

Which one of the schedules below is the correct serialization of the above?

(A) T1 T3 T2→ → (B) T2 T1 T3→ →

(C) T2 T3 T1→ → (D) T3 T1 T2→ →

43. The following functional dependencies hold for relations R(A, B, C) and S(B, D, E)

B A,A C

→→

The relation R contains 200tuples and the relation S contains 100tuples. What is

the maximum number of tuples possible in the natural join R S?

(A) 100 (B) 200 (C) 300 (D) 2000




44. The following program is to be tested for statement coverage:

( ) ( )

= == =

begin

if a b S1; exit;

else if c d S2;

else S3; exit;

S4;end

The test cases T1, T2, T3 and T4 given below are expressed in terms of the

properties satisfied by the values of variables a, b, c and d. The exact values are not given.

T1 : a, b, c and d are all equal

T2 : a, b, c and d are all distinct

T3 : a=b and c !=d

T4 : a !=b and c=d

Which of the test suites given below ensures coverage of statements S1, S2, S3

and S4?

(A) T1, T2, T3 (B) T2, T4 (C) T3, T4 (D) T1, T2, T4

45. The following program consists of 3 concurrent processes and 3 binary

semaphores. The semaphores are initialized as S0=1, S1=0, S2=0.

Process P0 Process P1 Process P2

while (true)

wait (S0);

print ‘0’

release (S1);

release (S2);

wait (S1);

Release (S0);

wait (S2);

release (S0);

How many times will process P0 print ‘0’?

(A) At least twice (B) Exactly twice (C) Exactly thrice (D) Exactly once

46. A system has n resources R0,…,Rn-1, and k processes P0,…..Pk-1. The

implementation of the resource request logic of each process Pi. is as follows:

i

i+2

n-i

n-i-2

if (i% 2==0)

if (i<n) request R ;

if (i+2<n)request R ;

else

if (i<n) request R ;

if (i+2<n)request R ;

In which one of the following situations is a deadlock possible?

(A) n 40,k 26= = (B) n 21,k 12= = (C) n 20,k 10= = (D) n 41,k 19= =




47. Suppose computers A and B have IP addresses 10.105.1.113 and 10.105.1.91

respectively and they both use the same net mask N. Which of the values of N

given below should not be used if A and B should belong to the same network?

(A) 255.255.255.0 (B) 255.255.255.128

(C) 255.255.255.192 (D) 255.255.255.224


A computer system has an L1 cache, an L2 cache, and a main memory unit

connected as shown below. The block size in L1 cache is 4 words. The block size

in L2 cache is 16 words. The memory access times are 2 nanoseconds.

20 nanoseconds and 200 nanoseconds for L1 cache, L2 cache and main memory unit respectively.

48. When there is a miss in L1 cache and a hit in L2 cache, a block is transferred from L2 cache to L1 cache. What is the time taken for this transfer?

(A) 2 nanoseconds (B) 20 nanoseconds

(C) 22 nanoseconds (D) 88 nanoseconds

49. When there is a miss in both L1 cache and L2 cache, first a block is transferred

from main memory to L2 cache, and then a block is transferred from L2 cache to L1 cache. What is the total time taken for these transfers?

(A) 222 nanoseconds (B) 888 nanoseconds

(C) 902 nanoseconds (D) 968 nanoseconds


Consider a complete undirected graph with vertex set 0, 1, 2, 3, 4. Entry Wij in

the matrix W below is the weight of the edge i, j.

0 1 8 1 4

1 0 12 4 9

W 8 12 0 7 3

1 4 7 0 2

4 9 3 2 0

=

50. What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?

(A) 7 (B) 8 (C) 9 (D) 10

51. What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this

graph such that P contains at most 3 edges?

(A) 7 (B) 8 (C) 9 (D) 10

L1Cache

L2Cache

MainMemory

4 words

Data Bus

4 words

Data Bus






A hash table of length 10 uses open addressing with hash function h(k)=k

mod 10, and linear probing. After inserting 6 values into an empty hash table,

the table is as shown below

0

1

2 42

3 23

4 34

5 52

6 46

7 33

8

9

52. Which one of the following choices gives a possible order in which the key values

could have been inserted in the table?

(A) 46, 42, 34, 52, 23, 33 (B) 34, 42, 23, 52, 33, 46

(C) 46, 34, 42, 23, 52, 33 (D) 42, 46, 33, 23, 34, 52

53. How many different insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above?

(A) 10 (B) 20 (C) 30 (D) 40


Consider a network with 6 routers R1 to R6 connected with links having

weights as shown in the following diagram

54. All the routers use the distance vector based routing algorithm to update their

routing tables. Each router starts with its routing table initialized to contain an

entry for each neighbour with the weight of the respective connecting link.

After all the routing tables stabilize, how many links in the network will never be used for carrying any data?

(A) 4 (B) 3 (C) 2 (D) 1

R4R2

R1

R3R5

R6

7

6

3

2 1

8

4

9




55. Suppose the weights of all unused links in the previous question are changed

to 2 and the distance vector algorithm is used again until all routing tables

stabilize. How many links will now remain unused?

(A) 0 (B) 1 (C) 2 (D) 3


56. Choose the most appropriate word from the options given below to the complete the following sentence:

His rather casual remarks on politics ___________ his lack of seriousness about

the subject.

(A) masked (B) belied (C) betrayed (D)suppressed

57. Which of the following options is closest in meaning to the word Circuitous.

(A) cyclic (B) indirect (C) confusing (D) crooked

58. Choose the most appropriate word from the options given below to complete the

following sentence:

If we manage to ____________ our natural resources, we would leave a better planet for our children.

(A) uphold (B) restrain (C) cherish (D) conserve

59. 25 persons are in a room. 15 of them play hockey, 17 of them play football and

10 of them play both hockey and football. Then the number of persons playing

neither hockey nor football is:

(A) 2 (B) 17 (C) 13 (D) 3

60. The question below consists of a pair of related words followed by four pairs of

words. Select the pair that best expresses the relation in the original pair.

Unemployed: Worker

(A) fallow: land (B) unaware: sleeper (C) wit: jester (D) renovated:house


61. If 137+276=435 how much is 731+672?

(A) 534 (B) 1403 (C) 1623 (D)1513

62. Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters).

All were born on 1st january. The age difference between any two successive

siblings (that is born one after another) is less than 3 years. Given the following facts:

i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age

ii. The age difference between Gita and Saira is 1 year. However Gita is not the

oldest and Saira is not the youngest.

iii. There are no twins.




In what order were they born (oldest first)?

(A) HSIG (B) SGHI (C) IGSH (D) IHSG

64. 5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a wall

in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

(A) 20 (B) 18 (C) 16 (D) 15

63. Modern warfare has changed from large scale clashes of armies to suppression of

civilian populations. Chemical agents that do their work silently appear to be

suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.

Which of the following statements best sums up the meaning of the above passage:

(A) Modern warfare has resulted in civil strife.

(B) Chemical agents are useful in modern warfare.

(C) Use of chemical agents in warfare would be undesirable

(D) People in military establishments like to use chemical agents in war.

65. Given digits 2,2,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000 can be formed?

(A) 50 (B) 51 (C) 52 (D) 54

|CS-GATE-2013 PAPER|

India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India

1


1. Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is ½. What is the expected number of unordered cycles of length three?

(A) 1/8 (B) 1 (C) 7 (D) 8

Answer:-(C)

Exp:- 1

P(edge)2

=

Number of ways we can choose the vertices out of 8 is 3c8

(Three edges in each cycle)

Expected number of unordered cycles of length 3 =3

3

C

18 7

2

× =

2. Which of the following statements is/are TRUE for undirected graphs?

P: Number of odd degree vertices is even.

Q: Sum of degrees of all vertices is even.

(A) P only (B) Q only

(C) Both P and Q (D) Neither P nor Q

Answer:- (C)

Exp:- Q: Sum of degrees of all vertices ( )2 number of edges= ×

3. Function f is known at the following points:

x 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0

f(x) 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00

The value of ( )3

0f x dx∫ computed using the trapezoidal rule is

(A) 8.983 (B) 9.003 (C) 9.017 (D) 9.045

Answer:- (D)

Exp:- ( ) ( ) ( ) ( ) ( ) ( )( )3

0 10 1 2 9

0

hf x dx f x f x 2 f x f x ... f x

2 = + + + + + ∫

( )0.39.00 2 25.65 9.045

2= + =



2

4. Which one of the following functions is continuous at x = 3 ?

( ) ( )2, if x 3

A f x x 1, if x 3

x 3, if x 3

3

=

= − > + <

( ) ( )4, if x 3

B f x8 x if x 3

==

− ≠

( ) ( )x 3, if x 3

C f xx 4 if x 3

+ ≤=

− > ( ) ( ) 3

1D f x , if x 3

x 27= ≠

−

Answer:-(A)

Exp:- ( ) ( ) ( )x 3 x 3lim f x lim x 1 2 f 3→ + → +

= − = =

( ) ( )

( )x 3 x 3

x 3lim f x lim 2 f 3

3

f x is continuous at x 3

→ − → −

+ = = =

∴ =

5. Which one of the following expressions does NOT represent exclusive NOR of x and y?

(A) xy x 'y '+ (B) x y'⊕ (C) x ' y⊕ (D) x ' y '⊕

Answer: -(D)

Exp:- (A) x y xy x y= +

( )B x y xy x y xy x y x y⊕ = + = + =

( ) ( )C x y x y x y x y xy x y⊕ = + = + =

( ) ( )D x y x y x y x y⊕ = + = ⊕

6. In a k-way set associative cache, the cache is divided into v sets, each of which consists of k lines. The lines of a set are placed in sequence one after another. The lines in set s are sequenced before the lines in set (s+1). The main memory blocks are numbered 0 onwards. The main memory block numbered j must be mapped to any one of the cache lines from

(A) ( ) ( ) ( )j mod v *k to j mod v *k k 1+ −

(B) ( ) ( ) ( )j mod v to j mod v k 1+ −

(C) ( ) ( ) ( )j mod k to j mod k v 1+ −

(D) ( ) ( ) ( )j mod k * v to j mod k * v v 1+ −

Answer: -(A)

Exp:- Position of main memory block in the cache (set) = (main memory block number) MOD (number of sets in the cache).

As the lines in the set are placed in sequence, we can have the lines from 0 to (K – 1) in each set.

Number of sets = v, main memory block number = j

First line of cache = (j mod v)*k; last line of cache = (j mod v)*k + (k – 1)



3

7. What is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices?

(A) ( )2nΘ (B) ( )2n log nΘ (C) ( )3nΘ (D) ( )3n log nΘ

Answer:-(C)

Exp:- Bellman-ford time complexity: ( V E )Θ ×

For complete graph: n(n 1)

E2

−=

3

V n

n(n 1)n (n )

2

=

− ∴Θ × = Θ


(1) The problem of determining whether there exists a cycle in an undirected graph is in P.

(2) The problem of determining whether there exists a cycle in an undirected graph is in NP.

(3) If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.

(A) 1,2 and 3 (B) 1 and 2 only (C) 2 and 3 only (D) 1 and 3 only

Answer: -(A)

Exp:- 1. Cycle detection using DFS: 2O(V E) O(V )+ = and it is polynomial problem

2. Every P-problem is NP ( )since P NP⊂

3. NP complete NP− ∈

Hence, NP-complete can be solved in non-deterministic polynomial time

9. Which of the following statements is/are FALSE?

(1) For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine.

(2) Turing recognizable languages are closed under union and complementation.

(3) Turing decidable languages are closed under intersection and complementation

(4) Turing recognizable languages are closed under union and intersection.

(A) 1 and 4 only (B) 1 and 3 only (C) 2 only (D) 3 only

Answer: -(C)

Exp:- (1) NTM ≅ DTM

(2) RELs are closed under union & but not complementation

(3) Turing decidable languages are recursive and recursive languages are closed under intersection and complementation

(4) RELs are closed under union & intersection but not under complementation



4

10. Three concurrent processes X, Y, and Z execute three different code segments that access and update certain shared variables. Process X executes the P operation (i.e., wait) on semaphores

a, b and c; process Y executes the P operation on semaphores b, c and d; process Z executes the P operation on semaphores c, d, and a before entering the respective code segments. After completing the execution of its code segment, each process invokes the V operation (i.e.,

signal) on its three semaphores. All semaphores are binary semaphores initialized to one. Which one of the following represents a deadlock-free order of invoking the P operations by the processes?

(A) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )X : P a P b P c Y : P b P c P d Z: P c P d P a

(B) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )X : P b P a P c Y : P b P c P d Z: P a P c P d

(C) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )X : P b P a P c Y : P c P b P d Z: P a P c P d

(D) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )X : P a P b P c Y : P c P b P d Z: P c P d P a

Answer:-(B)

Exp:- Suppose X performs P(b) and preempts, Y gets chance, but cannot do its first wait i.e., P(b), so waits for X, now Z gets the chance and performs P(a) and preempts, next X gets chance. X cannot continue as wait on ‘a’ is done by Z already, so X waits for Z. At this time Z can continue its operations as down on c and d. Once Z finishes, X can do its operations and so Y.

In any of execution order of X, Y, Z one process can continue and finish, such that waiting is not circular. In options (A),(C) and (D) we can easily find circular wait, thus deadlock

11. An index is clustered, if

(A) it is on a set of fields that form a candidate key

(B) it is on a set of fields that include the primary key

(C) the data records of the file are organized in the same order as the data entries of the index

(D) the data records of the file are organized not in the same order as the data entries of the index

Answer:-(C)

Exp:- Clustered index is built on ordering non key field and hence if the index is clustered then the data records of the file are organized in the same order as the data entries of the index.

12. Assume that source S and destination D are connected through two intermediate routers labeled R. Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D.

(A) Network layer – 4 times and Data link layer-4 times

(B) Network layer – 4 times and Data link layer-3 times

(C) Network layer – 4 times and Data link layer-6 times

(D) Network layer – 2 times and Data link layer-6 times

S R R D



5

Answer:-(C)

Exp:-

From above given diagram, its early visible that packet will visit network layer 4 times, once

at each node [S, R, R, D] and packet will visit Data Link layer 6 times. One time at S and one

time at D, then two times for each intermediate router R as data link layer is used for link to

link communication.

Once at packet reaches R and goes up from physical –DL-Network and second time when

packet coming out of router in order Network – DL- Physical

13. The transport layer protocols used for real time multimedia, file transfer, DNS and

email, respectively are

(A) TCP, UDP, UDP and TCP (B) UDP, TCP, TCP and UDP

(C) UDP, TCP, UDP and TCP (D) TCP, UDP, TCP and UDP

Answer:- (C)

Exp:- Real time multimedia needs connectionless service, so under lying transport layer protocol

used is UDP

File transfer rums over TCP protocol with port no-21

DNS runs over UDP protocol within port no-53

Email needs SMTP protocol which runs over TCP protocol within port no – 25

14. Using public key cryptography, X adds a digital signature σ to message M, encrypts <M,

σ >, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is

used for the operations?

(A) Encryption: X’s private key followed by Y’s private key; Decryption: X’s public key

followed by Y’s public key

(B) Encryption: X’s private key followed by Y’s public key; Decryption: X’s public key

followed by Y’s private key

(C) Encryption: X’s public key followed by Y’s private key; Decryption: Y’s public key

followed by X’s private key

(D) Encryption: X’s private key followed by Y’s public key; Decryption: Y’s private key

followed by X’s public key

Application

Transport

Network

Datalink

Physical

Network

DataLink

Physical

Network

DataLink

Physical

Application

Transport

Network

Datalink

Physical

( )Source

S R R

( )Destination

D



6

Answer:-(D)

Exp:-

15. Match the problem domains in Group I with the solution technologies in Group II.

Group I Group II

(p) Services oriented computing (1) Interoperability

(q) Heterogeneous communicating systems (2) BPMN

(R) Information representation (3) Publish-find bind

(S) Process description (4) XML

(A) P – 1, Q – 2, R – 3, S – 4 (B) P – 3, Q – 4, R – 2, S – 1

(C) P – 3, Q – 1, R – 4, S – 2 (D) P – 4, Q – 3, R – 2, S – 1

Answer:-(C)

16. A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero(the lowest priority). The scheduler re-evaluates the process priorities every T time units and decides the next process to schedule. Which one of the following is TRUE if the processes have no I/O operations and all arrive at time zero?

(A) This algorithm is equivalent to the first-come-first-serve algorithm

(B) This algorithm is equivalent to the round-robin algorithm

(C) This algorithm is equivalent to the shortest-job-first algorithm

(D) This algorithm is equivalent to the shortest-remaining-time-first algorithm

Answer:-(B)

Exp:- The given scheduling definition takes two parameters, one is dynamically assigned process priority and the other is ‘T’ time unit to re-evaluate the process priorities.

This dynamically assigned priority will be deciding processes order in ready queue of round robin algorithm whose time quantum is same as ‘T’ time units. As all the processes are arriving at the same time, they will be given same priority but soon after first ‘T’ time burst remaining processes will get higher priorities

X Y

X public

X private

−

−

Y public

Y private

−

−

σ

Source has to encrypt with its pr ivate key for

forming Digital signature for Authentication.Encryption

source has to encrypt the M, with Y 's

public key to send it confidentially

Destination Y has to decrypt first

Decryption wit

h its private key, then decrypt

using source public key



7

17. What is the maximum number of reduce moves that can be taken by a bottom-up parser for a

grammar with no epsilon- and unit-production ( )i.e., of type A and A a→ ∈ → to parse a

string with n tokens?

(A) n/2 (B) n-1 (C) 2n-1 (D) 2n

Answer: -(B)

Exp:- To have maximum number of reduce moves, all the productions will be of the typeA→αβ

(where α and β could be terminals or non-terminals). Consider the following illustration

then:

1 2 3 n 2 n 1 n

1 2 3 n 2

1 2 3

1 2

InputString : a a a ........ a a a

a a a ........... a A

a a a ..................A n 1 moves

a a

A

− −

−

↑

−

↑

18. Consider the languages 1 2L and L a= Φ = . Which one of the following represents

* *1 2 1L L UL ?

(A) ∈ (B) Φ (C) a * (D) , aε

Answer: -(A)

Exp:- Concatenation of empty language with any language will give the empty language and

1L * *= Φ =∈. Hence * *1 2 1L L UL = ∈

19. Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes?

(A) O(1) (B) O(log n) (C) O(n) (D) O(n log n)

Answer:-(C)

Exp:- For skewed binary search tree on n nodes, the tightest upper bound to insert a node is O(n)

20. Which one of the following is the tightest upper bound that represents the number of swaps

required to sort n numbers using selection sort?

(A) O(log n) (B) O(n) (C) O(n log n) (D) O(n2)

Answer:-(B)

Exp:- The maximum number of swaps that takes place in selection sort on n numbers is n



8

21. In the following truth table, V = 1 if and only if the input is valid.

Inputs Outputs

D0 D1 D2 D3 X0 X1 V

0 0 0 0 X X 0

1 0 0 0 0 0 1

X 1 0 0 0 1 1

X X 1 0 1 0 1

X X X 1 1 1 1

What function does the truth table represent?

(A) Priority encoder (B) Decoder

(C) Multiplexer (D) Demultiplexer

Answer: -(A)

Exp:- 4 to 2 priority encoder.

22. The smallest integer than can be represented by an 8-bit number in 2’s complement form is

(A) -256 (B) -128 (C) -127 (D) 0

Answer: -(B)

Exp:- 8 12 128−− = − . Range is -2(n-1) to +2(n-1)-1

23. Which one of the following does NOT equal

2

2

2

1 x x

1 y y ?

1 z z

( )( )( )( )

1 x x 1 x 1

A 1 y y 1 y 1

1 z z 1 z 1

+ +

+ +

+ +

( )

2

2

2

1 x 1 x 1

B 1 y 1 y 1

1 z 1 z 1

+ +

+ +

+ +

( )

2 2

2 2

2

0 x y x y

C 0 y z y z

1 z z

− −

− − ( )

2 2

2 2

2

2 x y x y

D 2 y z y z

1 z z

+ +

+ +

Answer:- (A)

Exp:- If matrix B is obtained from matrix A by replacing the lth row by itself plus k times the mth row, for l m≠ then det(B)=det(A). With this property given matrix is equal to the matrices given in options (B),(C) and (D).

24. Suppose p is number of cars per minute passing through a certain road junction between 5 PM and 6PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

(A) ( )38 / 2e (B) ( )39 / 2e (C) ( )317 / 2e (D) ( )326 / 2e



9

Answer:-(C)

Exp:- ( ) ( ) ( ) ( )P p 3 P p 0 P p 1 P p 2< = = + = + =

( )0 1 2

33 3

3

3

e e ewhere 3

0! 1! 2!

e 9e e 3

2

9 17e 1 3

2 2e

−λ −λ −λ

−− −

−

λ λ λ= + + λ =

×= + × +

= + + =

25. A binary operation ⊕ on a set of integers is defined as 2 2x y x y⊕ = + . Which one of the

following statements is TRUE about ⊕ ?

(A) Commutative but not associative (B) Both commutative and associative

(C) Associative but not commutative (D) Neither commutative nor associative

Answer:- (A)

Exp:- 2 2 2 2x y x y y x y x

commutative

⊕ = + = + = ⊕

∴

Not associative, since, for example

( ) ( )1 2 3 1 2 3⊕ ⊕ ≠ ⊕ ⊕


26. Which one of the following is NOT logically equivalent to ( ) ( )( )x y z ?¬∃ ∀ α ∧ ∀ β

(A) ( ) ( )( )x z y∀ ∃ ¬β → ∀ α (B) ( ) ( )( )x z y∀ ∀ β → ∃ ¬α

(C) ( ) ( )( )x y z∀ ∀ α → ∃ ¬β (D) ( ) ( )( )x y z∀ ∃ ¬α → ∃ ¬β

Answer: -(A) and (D) [marks to all]

Exp:- ( ) ( )( )x y z¬∃ ∀ α ∧ ∀ β

( ) ( ) ( )( ) ( ) [ ]

y z option "C" p q p q

x z y option "B" p q q p

≡∀× ∀ α →∃ ¬β ¬ ∧ ≡ ⇒¬

≡∀ ∀ β → ∃ ¬α ⇒ ≡¬ ⇒¬

∵

∵

27. A RAM chip has a capacity of 1024 words of 8 bits each ( )1K 8× . The number of 2 4×

decoders with enable line needed to construct a 16K 16 RAM from 1K 8 RAM× × is

(A) 4 (B) 5 (C) 6 (D) 7

Answer: -(B)



10

Exp:- RAM chip size = [ ]1k 8 1024 words of 8 bits each×

RAM to construct 16k 16= ×

Number of chips required = 16k 16

16 21k 8

×= ×

× [16 chips vertically with each having 2 chips

horizontally]

So to select one chip out of 16 vertical chips, we need 4 x 16 decoder.

Available decoder is – 2 x 4 decoder

To be constructed is 4 x 16 decoder

So we need 5, 2 x 4 decoder in total to construct 4 x 16 decoder.

28. Consider an instruction pipeline with five stages without any branch prediction: Fetch

Instruction (FI), Decode Instruction (DI), Fetch Operand (FO), Execute Instruction (EI) and

Write Operand (WO). The stage delays for FI, DI, FO, EI and WO are 5 ns, 7 ns, 10 ns, 8 ns

and 6 ns, respectively. There are intermediate storage buffers after each stage and the delay of

each buffer is 1 ns. A program consisting of 12 instructions 1 2 3 12I , I , I ,......I is executed in this

pipelined processor. Instruction 4I is the only branch instruction and its branch target is 9I . If

the branch is taken during the execution of this program, the time (in ns) needed to complete

the program is

(A) 132 (B) 165 (C) 176 (D) 328

Answer: - (B)

Exp:- Clock period=Maximum stage delay+ overhead (Buffer) =10+1=11 ns

Assume FI-1, DI-2, FO-3, EI-4, WO-5



11

So number of clocks required to complete the program is = 15 clocks and time taken is = 15 ×11 ns=165 ns.

29. Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter

( )

( ) ( )( )

MultiDequeue Q

m k

while Q is not empty and m 0

Dequeue Q

m m 1

=

>

= −

What is the worst case time complexity of a sequence of n queue operations on an initially empty queue?

(A) ( )nΘ (B) ( )n kΘ + (C) ( )nkΘ (D) ( )2nΘ

Answer:- (A)

Exp:- Initially the queue is empty and we have to perform n operations.

i) One option is to perform all Enqueue operations i.e. n Enqueue operations. Complexity will be θ(n)

or

ii) We can perform a mix of Enqueue and Dequeue operations. It can be Enqueue for first n/2 times and then Dequeue for next n/2, or Enqueue and Dequeue alternately, or any permutation of Enqueues and Dequeues totaling ‘n’ times. Complexity will be θ(n)

or

iii) We can perform Enqueues and MultiDequeues. A general pattern could be as follows:

1

2

3

4

5

6

7

8

9

10

11

12

I : 1 2 3 4 5

I : 1 2 3 4 5

I : 1 2 3 4 5

I : 1 2 3 4 5

I : 1 2 3 4 5

I : 1 2 3 4 5

I : 1 2 3 4 5

I : 1 2 3 4 5

I : 1 2 3 4 5

I : 1 2 3 4 5

I 1 2 3 4 5

I 1 2 3 4 5

−

− −

− − −

− − − −

− − − − −

− − − − − −

− − − − − − −

− − − − − − − −

− − − − − − − − −

− − − − − − − − − −

− − − − − − − − − − −



12

Enqueue Enqueue … (ktimes) MultiDequeue Enqueue Enqueue … (ktimes) MultiDequeue … Up to total n

---- k items enqueued -----k items deleted----k items enqueued----k items deleted -- and so on.

The number of times this k-Enqueues, MutiDequeue cycle is performed = nk 1+

So, Complexity will be k times Enqueue + 1 MultiDequeue) nk 1

× +

Which is ( ) ( )n2k nk 1

θ × = θ+

or

iv) We can just perform n MultiDequeues (or n Dequeues for that matter):

Each time the while condition is false (empty queue), condition is checked just once for each of the ‘n’ operations. So θ(n).

30. The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42. Which one of the following is the postorder traversal sequence of the same tree?

(A) 10,20,15,23,25,35,42,39,30 (B) 15,10,25,23,20,42,35,39,30

(C) 15,20,10,23,25,42,35,39,30 (D) 15,10,23,25,20,35,42,39,30

Answer:-(D)

Exp:- Pr eorder :30,20,10,15,25,23,39,35,42

Inorder :10,15,20,23,25,30,35,39,42

31. What is the return value of ( )f p,p if the value of p is initialized to 5 before the call? Note

that the first parameter is passed by reference, whereas the second parameter is passed by value.

( )

( )

( )

int f int & x, int c

c c 1;

if c 0 return 1;

x x 1;

return f x,c * x;

= −==

= +

(A) 3024 (B) 6561 (C) 55440 (D) 161051

30

3920

10

15

25

23

35 42

BST :



13

Answer:-(B)

Exp:-

32. Which of the following is/are undecidable?

1. G is a CFG. Is ( )L G ?= Φ

2. G is a CFG. IS ( )L G *?= Σ

3. M is a Turning machine. Is L(M) regular?

4. A is a DFA and N is a NFA. Is ( ) ( )L A L N ?=

(A) 3 only (B) 3 and 4 only (C) 1, 2 and 3 only (D) 2 and 3 only

Answer: -(D)

Exp:- There is an algorithm to check whether the given CFG is empty, finite or infinite and also to

convert NFA to DFA hence 1 and 4 are decidable

33. Consider the following two sets of LR(1) items of an LR(1) grammar

X c.X, c / d X c.X, $

X .cX, c / d X .cX, $

X .d, c / d X .d, $

→ →→ →→ →

Which of the following statements related to merging of the two sets in the corresponding

LALR parser is/are FALSE?

1. Cannot be merged since look aheads are different

2. Can be merged but will result in S–R conflict

3. Can be merged but will result in R–R conflict

4. Cannot be merged since goto on c will lead to two different sets

(A) 1 only (B) 2 only (C) 1 and 4 only (D) 1, 2, 3 and 4

( )( )

( )

( )

( )

( )

( )

( )

( )

f x, 5

1

f x, 4 x

2

f x, 3 x

3

f x, 2 x

4

f x, 1 x

⇓

×

⇓

×

⇓

×

⇓

×

9

6

7 8

9

9

9 9×

9 9 9× ×

9 9 9 9

6561

× × ×

=



14

Answer:-(D)

Exp:-

1. Merging of two states depends on core part (production rule with dot operator), not on look aheads.

2. The two states are not containing Reduce item ,So after merging, the merged state can not contain any S-R conflict

3. As there is no Reduce item in any of the state, so can’t have R-R conflict.

4. Merging of stats does not depend on further goto on any terminal.

So all statements are false.

34. A certain computation generates two arrays a and b such that [ ] ( )a i f i for 0 i n= ≤ < and

[ ] [ ]( )b i g a i for 0 i n= ≤ < . Suppose this computation is decomposed into two concurrent

processes X and Y such that X computes the array a and Y computes the array b. The processes employ two binary semaphores R and S, both initialized to zero. The array a is shared by the two processes. The structures of the processes are shown below.

( ) ( )[ ] ( ) ( )

( ) [ ] [ ]( )

Pr ocess X; Pr ocess Y;

private i; private i;

for i 0; i n; i for i 0; i n; i

a i f i ; EntryY R, S ;

ExitX R, S ; b i g a i ;

= < + + = < + +

=

=

Which one of the following represents the CORRECT implementations of ExitX and EntryY?

(A) ( )( )( )

( )( )( )

ExitX R, S

P R ;

V S ;

EntryY R, S

P S ;

V R ;

(B) ( )( )( )

( )( )( )

ExitX R, S

V R ;

V S ;

EntryY R, S

P R ;

P S ;

x c.X,c / d

x .cX,c / d

x .d,c / d

→

→

→

x c.X,$

x .cX,$

x .d,$

→

→

→

x c.X,c / d /$

x .cX,c / d /$

x .d, c / d /$

→

→

→



15

(C) ( )( )( )

( )( )( )

ExitX R, S

P S ;

V R ;

EntryY R, S

V S ;

P R ;

(D) ( )( )( )

( )( )( )

ExitX R, S

V R ;

P S ;

EntryY R, S

V S ;

P R ;

Answer:-(C)

Exp:- For computing both the array a[] and b[], first element a[i] should be computed using which b[i] can be computed. So process X and Y should run in strict alteration manner, starting with X. This requirement meets with implementation of ExitX and EntryY given in option C.

35. The following figure represents access graphs of two modules M1 and M2. The filled circles represent methods and the unfilled circles represent attributes. IF method m is moved to module M2 keeping the attributes where they are, what can we say about the average cohesion and coupling between modules in the system of two modules?

(A) There is no change

(B) Average cohesion goes up but coupling is reduced

(C) Average cohesion goes down and coupling also reduces

(D) Average cohesion and coupling increase

Answer:-(A)

Exp:-

1 2

number of external links 2Coupling =

number of modules 2

number of internal linksCohesion of a module =

number of methods

8 6Cohesion of M = ; Cohesion of M = ; Average cohesion=2

4 3

=

Module M1 Module M2

m

Module M1 Module M2

m



16

After moving method m to M2, graph will become

1 2

2Coupling

2

6 8Cohesion of M = ; Cohesion of M = ; Average cohesion=2

3 4

answer is no change

=

∴

36. In an IPv4 datagram, the M bit is 0, the value of HLEN is 10, the value of total length is 400 and the fragment offset value is 300. The position of the datagram, the sequence numbers of the first and the last bytes of the payload, respectively are

(A) Last fragment, 2400 and 2789 (B) First fragment, 2400 and 2759

(C) Last fragment, 2400 and 2759 (D) Middle fragment, 300 and 689

Answer:-(C)

Exp:- M= 0 – Means there is no fragment after this, i.e. Last fragment

HLEN=10 - So header length is 4×10=40, as 4 is constant scale factor

Total Length = 400(40 Byte Header + 360 Byte Payload)

Fragment Offset = 300, that means 300×8 Byte = 2400 bytes are before this last fragment

So the position of datagram is last fragment

Sequence number of First Byte of Payload = 2400 (as 0 to 2399 Sequence no are used)

Sequence number of Last Byte of Payload = 2400+360-1=2759

37. Determine the maximum length of cable (in km) for transmitting data at a rate of 500 Mbps in an Ethernet LAN with frames of size 10,000 bits. Assume the signal speed in the cable to be 2,00,000 km/s

(A) 1 (B) 2 (C) 2.5 (D) 5

Answer:-(B)

Exp:- 6500 10 bits 1 sec× − − − − − −

8 44

4 8 4

5

5

4 4

5 10 10 110 bits sec sec

10 5 10 5 10

1 sec 2 10 km

1 2 10sec 4km

5 10 5 104

Maximum length of cable 2 km2

×∴ − − − − − − = =

× ×− − − − − − ×

×∴ − − − − − =

× ×

∴ = =

Module M1 Module M2

m



17

38. Consider the following relational schema.

Students(rollno: integer, sname: string)

Courses(courseno: integer, cname: string)

Registration(rollno: integer, courseno; integer, percent: real)

Which of the following queries are equivalent to this query in English?

“Find the distinct names of all students who score more than 90% in the course numbered 107”

(I) SELECT DISTINCT S.sname

FROM Students as S, Registration as R

WHERE R.rollno=S.rollno AND R.Courseno=107 AND R.percent>90

(II) ( )( )sname courseno 107 percent 90 Re gistration Students=Π σ ∧ >

(III) T | S Students, R Registration (S.rolln o R.rolln o∃ ∈ ∃ ∈ = ∧

R.courseno 107 R.percent 90 T.sname S.name)= ∧ > ∧ =

(IV) ( ) N R P R N R P PS | S R S ,S Stu de nts S ,107,R Re gistration R 90< > ∃ ∃ < >∈ ∧ < >∈ ∧ >

(A) I, II, III and IV (B) I, II and III only

(C) I, II and IV only (D) II, III and IV only

Answer:- (A)

Exp:- Four queries given in SQL, RA, TRC and DRC in four statements respectively retrieve the required information.

39. A shared variable x, initialized to zero, is operated on by four concurrent processes W, X, Y, Z as follows. Each of the processes W and X reads x from memory, increments by one, stores it to memory, and then terminates. Each of the processes Y and Z reads x from memory, decrements by two, stores it to memory, and then terminates. Each process before reading x invokes the P operation (i.e., wait) on a counting semaphore S and invokes the V operation (i.e., signal) on the semaphore S after storing x to memory. Semaphore S is initialized to two. What is the maximum possible value of x after all processes complete execution?

(A) –2 (B) –1 (C) 1 (D) 2

Answer:-(D)

Exp:-

W X Y Z

1 ( )R x ( )R x ( )R x ( )R x

2 x++ x++ x=x-2; x=x-2;

3 w(x) w(x) w(x) w(x)

R(x) is to read x from memory, w(x) is to store x in memory

(I) ( ) [ ]1w x 0 W is Preempted

(II) ( ) [ ]1 2 3Y ,Y ,Y x 2 Y is completed−



18

(III) ( ) [ ]1 2 3Z , Z , Z x 4 Z is completed−

(IV) ( ) [ ]2 3W , W x 1 It increments local copy of x and stores & W is completed

(V) ( ) [ ]1 2 3X ,X ,X x 2 X is completed

Maximum value of x = 2

40. Consider the DFA given below.

Which of the following are FALSE?

1. Complement of L(A) is context–free

2. ( ) ( )( )( )L A L 11* 0 0 0 1 * 0 *1*= + +

3. For the language accepted by A, A is the minimal DFA

4. A accepts all strings over 0, 1 of length at least 2

(A) 1 and 3 only (B) 2 and 4 only (C) 2 and 3 only (D) 3 and 4 only

Answer: - (D)

Exp:-

(1) L(A) is regular, its complement is also regular and if it is regular it is also context free.

(2) ( ) ( )( ) ( )L A 11*0 0 0 1 * 0*1* 1*0 0 1 *= + + = +

Language has all strings where each string contains ‘0’.

(3) A is not minimal, it can be constructed with 2 states

(4) Language has all strings, where each string contains ‘0’. (atleast length one)

1

00

0,1

1

1

0

0, 1

0

1

A :



19

41. Consider the following languages

p q r1

p q r2

L 0 1 0 | p,q, r 0

L 0 1 0 | p,q, r 0, p r

= ≥

= ≥ ≠

Which one of the following statements is FALSE?

(A) 2L is context–free

(B) 1 2L L∩ is context–free

(C) Complement of 2L is recursive

(D) Complement of 1L is context–free but not regular

Answer: -(D)

Exp:- P q r1L 0 1 0 p,q, r 0 is regular= ≥

P q r2L 0 1 0 p,q, r 0, p r is CFL= ≥ ≠

(A) ( )2L is CFL True

(B) ( )1 2L L CFL True∩ =

(C) ( )2L complement is recursive True

(D) ( ) 11 1L complement is CFL but not regular False as L is regular L is regular

42. Consider the following function

( )

( )( )

( )

int unknown int n

int i, j, k 0;

for i n / 2; i n; i

for j 2; j n; j j* 2

k k n / 2;

return k ;

== <= + +

= <= =

= +

The return value of the function is

(A) ( )2nΘ (B) ( )2n log nΘ (C) ( )3nΘ (D) ( )3n log nΘ

Answer:- (B)

Exp:- n n n

i , 1, 2, n2 2 2

= + + − − − − −

Repeats

n nto n 1 times

2 2

= +

( )( )

2 3 4J 2, 2 , 2 , 2 , n

k n log nnk k

2

= − − − − −

= Θ = +

n n n

k log n times log n2 2 2

= + + − − − − =



20

( )2

n n n nlog n log n log n 1 times

2 2 2 2

n n1 . log n

2 2

n log n

= + + − − − − +

= +

= Θ

43. The number of elements that can be sorted in ( )lognΘ time using heap sort is

(A) ( )1Θ (B) ( )log nΘ (C) log n

log log n

Θ

(D) ( )log nΘ

Answer:-(A)

Exp:- After constructing a max-heap in the heap sort , the time to extract maximum element and

then heapifying the heap takes ( )log nΘ time by which we could say that ( )log nΘ time is

required to correctly place an element in sorted array. If ( )lognΘ time is taken to sort using

heap sort, then number of elements that can be sorted is constant which is ( )1Θ

44. Consider a hard disk with 16 recording surfaces ( )0 15− having 16384 cylinders ( )0 16383−

and each cylinder contains 64 sectors ( )0 63− . Data storage capacity in each sector is 512

bytes. Data are organized cylinder–wise and the addressing format is <cylinder no., sector no.>. A file of size 42797 KB is stored in the disk and the starting disk location of the file is <1200, 9, 40>. What is the cylinder number of the last sector of the file, if it is stored in a contiguous manner?

(A) 1281 (B) 1282 (C) 1283 (D) 1284

Answer: -(D)

Exp:- 42797 1024

42797 KB 85594 sec tors512

×≡ =

Starting is 1200,9,40 contains total ( )24 6 64 408 sec tors+ × =

Next, 1201, --------, 1283 cylinders contains total 1024 83 84992 sec tors× =

( )each cylinder contains 16 64 1024 sec tors

Total 408 84992 85400 sec tors

× =

∴ = + =

∵

∴ The required cylinder number is 1284 which will contain the last sector of the file

45. Consider the following sequence of micro–operations

MBR PC

MAR X

PC Y

Memory MBR

←

←

←

←

Which one of the following is a possible operation performed by this sequence?

(A) Instruction fetch (B) Operand fetch

(C) Conditional branch (D) Initiation of interrupt service



21

Answer:-(D)

Exp:- PC content is stored in memory via MBR and PC gets new address from Y. It represents a function call (routine), which is matching with interrupt service initiation

46. The line graph L(G) of a simple graph G is defined as follows:

• There is exactly one vertex v(e) in L(G) for each edge e in G.

• For any two edges e and e’ in G, L(G) has an edge between v(e) and v(e’), if and only if e and e’ are incident with the same vertex in G.

Which of the following statements is/are TRUE?

(P) The line graph of a cycle is a cycle.

(Q) The line graph of a clique is a clique.

(R) The line graph of a planar graph is planar.

(S) The line graph of a tree is a tree.

(A) P only (B) P and R only

(C) R only (D) P, Q and S only

Answer: -(A)

Exp:- P) The line graph of a cycle is a cycle

R) Line graph of planar graph need not be planar always. Consider the following example.

Consider the following planar graph (star graph)

S) Hence line graph of planar graph need not be planar(Here we got K5 which is not planar).

ac

d

e f

b

1V(e )

2V(e )3V(e )

4V(e ) 5V(e )

1V(e )

5V(e )2V(e )

3V(e )4V(e )

( )L G :⇒

( )4V e

( )1V e

( )3V e

( )2V e

a b

d c

( )1V e

( )2V e

( )3V e

( )4V e ( )L G :⇒

is also cycle graph

G



22

The line graph of a tree need not be tree.

47. What is the logical translation of the following statement?

“None of my friends are perfect.”

(A) ( ) ( )( )x F x P x∃ ∧ ¬ (B) ( ) ( )( )x F x P x∃ ¬ ∧

(C) ( ) ( )( )x F x P x∃ ¬ ∧ ¬ (D) ( ) ( )( )x F x P x¬∃ ∧

Answer: -(D)

Exp:- “None of my friends are perfect”

( ) ( )( )( ) ( )( )( ) ( )( )

x F x P x

x F x P x

x F x P x

= ∀ →¬

= ∀ ¬ ∨ ¬

= ¬∃ ∧


The procedure given below is required to find and replace certain characters inside an input character string supplied in array A. The characters to be replaced are supplied in array oldc, while their respective replacement characters are supplied in array newc. Array A has a fixed length of five characters, while arrays oldc and newc contain three characters each. However, the procedure is flawed

( )( )

( )[ ] [ ]( ) [ ] [ ]

void find _ and _ replace char * A, char *oldc, char * newc

for int i 0; i 5; i

for int j 0; j 3; j

if A i oldc j A i newc j ;

= < + +

= < + +

== =

The procedure is tested with the following four test cases

(1) oldc "abc", newc "dab"= = (2) oldc "cde", newc "bcd"= =

(3) oldc "bca", newc "cda"= = (4) oldc "abc", newc "bac"= =

( )2V e

d c

( )3V e

( )1V e

( )2V e ( )3V e

b

a

( )1V e

( )L G :⇒



23

48. The tester now tests the program on all input strings of length five consisting of characters ‘a’, ‘b’, ‘c’, ‘d’ and ‘e’ with duplicates allowed. If the tester carries out this testing with the four test cases given above, how many test cases will be able to capture the flaw?

(A) Only one (B) Only two (C) Only three (D) All four

Answer:-(B)

Exp:- Flaw in this given procedure is that one character of Array ‘A’ can be replaced by more than one character of newc array, which should not be so.Test case (3) and (4) identifies this flaw as they are containing ‘oldc’ and ‘newc’ array characters arranged in specific manner. Following string can reflect flaw, if tested by test case (3).

initially i = j = 0

Next i = 0 & j = 1

Likewise single character ‘b’ in A is replaced by ‘c’ and then by ‘d’.

Same way test case (4) can also catch the flaw

49. If array A is made to hold the string “abcde”, which of the above four test cases will be successful in exposing the flaw in this procedure?

(A) None (B) 2 only (C) 3 and 4 only (D) 4 only

Answer:-(C)

Exp:- Now for string “abcde” in array A, both test case (3) and (4) will be successful in finding the flaw, as explained in above question.


The following code segment is executed on a processor which allows only register operands in its instructions. Each instruction can have almost two source operands and one destination operand. Assume that all variables are dead after this code segment

( )

c a b;

d c * a;

e c a;

x c *c;

if x a

y a * a;

else

d d * d;

e e * e;

= +== +=

>=

==

=A "b c da" =oldc "b c a"

↑

=j 0

↑

=i 0

=newc "c da"

↑

=j 0

=b b so replaced by c

=A "c c da" =oldc "b c a"

↑

=j 1

↑

=i 0

=newc "c da"

↑

=j 1

=c c so replaced by d



24

50. Suppose the instruction set architecture of the processor has only two registers. The only allowed compiler optimization is code motion, which moves statements from one place to another while preserving correctness. What is the minimum number of spills to memory in the compiled code?

(A) 0 (B) 1 (C) 2 (D) 3

Answer:- (B)

Exp:- After applying the code motion optimization the statement d=c*a; and e=c+a; can be moved down to else block as d and e are not used anywhere before that and also value of a and c is not changing.

c a b;= + 2 1 2R R R← +

x c*c;=

2 2 2R R * R← [ ]cspill

1 memory spill to store

the value of c in memory

( )if x a> 2 1CMP R R

y a *a;= 2 1 1R R * R←

else

d c *a ;

d d *d;

e c a;

e e*e;

=

=

= +

=

[ ]

[ ]

2 c

2 2 1

2 2 2

2 c

2 2 1

2 2 2

R spill

R R *R

R R *R

R spill

R R R

R R *R

←

←

←

←

← +

←

In the above code total number of spills to memory is 1

51. What is the minimum number of registers needed in the instruction set architecture of the processor to compile this code segment without any spill to memory? Do not apply any optimization other than optimizing register allocation

(A) 3 (B) 4 (C) 5 (D) 6

Answer:- (B)

Exp:-

c a b;= + 2 1 2R R R← +

d c*a ;= 3 2 1R R *R←

e c a;= + 4 2 1R R R← +

x c*c;= 2 2 2R R * R←



25

( )if x a> 2 1CMP R R

y a *a;= 1 1 1R R *R←

else

d d *d;

e e*e;

=

= 3 3 3

4 4 4

R R *R

R R *R

←

←

In the above code minimum number of registers needed are = 4



Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values.

F CH G, A BC, B CFH, E A, F EG= → → → → → is a set of functional dependencies

(FDs) so that F+ is exactly the set of FDs that hold for R

52. How many candidate keys does the relation R have?

(A) 3 (B) 4 (C) 5 (D) 6

Answer:-(B)

Exp:- Candidate keys are AD, BD, ED and FD

53. The relation R is

(A) in INF, but not in 2NF (B) in 2NF, but not in 3NF

(C) in 3NF, but not in BCNF (D) in BCNF

Answer:-(A)

Exp:- A BC,B CFH and F EG→ → → are partial dependencies. Hence it is in 1NF but not in 2NF


A computer uses 46–bit virtual address, 32–bit physical address, and a three–level paged page table organization. The page table base register stores the base address of the first–level table

( )1T ,which occupies exactly one page. Each entry of 1T stores the base address of a page of the

second–level table ( )2T . Each entry of 2T stores the base address of a page of the third–level table

( )3T Each entry of 3T stores a page table entry (PTE). The PTE is 32 bits in size. The processor

used in the computer has a 1 MB 16 way set associative virtually indexed physically tagged cache. The cache block size is 64 bytes.

54. What is the size of a page in KB in this computer?

(A) 2 (B) 4 (C) 8 (D) 16



26

Answer:-(C)

Exp:- Let the page size be X2 Bytes.

Then, the page offset = X bits

Now, we are using 3-level paging. First level page table is contained in one page. Each page table entry is 32-bit.

The size of T3 is = 46 2

46+2-x

x

2 * 2= 2

2 [ ∵PTE=32 bit = 4B = 22B ]

The size of T2 is = 46+2-x 2

46+4-2x

x

2 * 2= 2

2

The size of T1 is = 46+4-2x 2

46+6-3x

x

2 * 2= 2

2 = X2 [∵T1 occupies exactly one page]

∴ 46 6 3x x x 13+ − = ⇒ =

So, page size = 13 32 B 2 kB 8kB.= =

55. What is the minimum number of page colours needed to guarantee that no two synonyms map to different sets in the processor cache of this computer?

(A) 2 (B) 4 (C) 8 (D) 16

Answer:- (C)

Exp:- As the page size is 132 Bytes and page coloring is asked so we divide cache size by page size and group 16 pages in one set.

Number of pages in cache=1MB/8KB=128 pages

Number of set in cache=128/16=8 sets

Take any page of LAS, it will be mapped with cache on any one of these 8 sets (set association mapping).For any two synonym to map with same set they should be colored with same color of that respective set. So minimum we need 8 colors for this mapping.

46-x x

32

32

32

..........

..........



27


56. Complete the sentence:

Universalism is to particularism as diffuseness is to ________

(A) specificity (B) neutrality (C) generality (D) adaptation

Answer:-(A)

Exp:- The relation is that of antonyms

57. Were you a bird, you ___________ in the sky.

(A) would fly (B) shall fly

(C) should fly (D) shall have flown

Answer:-(A)

58. Which one of the following options is the closest in meaning to the word given below?

Nadir

(A) Highest (B) Lowest (C) Medium (D) Integration

Answer:-(B)

Exp:- Nadir in the lowest point on a curve

59. Choose the grammatically INCORRECT sentence:

(A) He is of Asian origin (B) They belonged to Africa

(C) She is an European (D) They migrated from India to Australia

Answer:-(C)

60. What will be the maximum sum of 44, 42, 40, ... ?

(A) 502 (B) 504 (C) 506 (D) 500

Answer:-(C)

Exp:- The maximum sum is the sum of 44, 42,- - - - -2.

The sum of ‘n’ terms of an AP

( )n2a n 1 d

2= + −

In this case, n = 22, a = 2 and d = 2

[ ]Sum 11 4 21 2 11 46 506∴ = + × = × =


61. Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

(A) 13/90 (B) 12/90 (C) 78/90 (D) 77/90



28

Answer:- (D)

Exp:- The number of 2 digit multiples of 7 = 13

∴ Probability of choosing a number

Not divisible by 90 13 77

790 90

−= =

62. A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average of the tourist in km/h during his entire journey is

(A) 36 (B) 30 (C) 24 (D) 18

Answer:- (C)

Exp:- Let the total distance covered be ‘D’

Now, average speed = D

Total time taken

D 1 120

24km / hr1 1 1D D D 5

120 120 402 4 460 30 10

= = = = + +

+ +

63. Find the sum of the expression

1 1 1 1

..... 1 2 2 3 3 4 80 81

+ + + ++ + + +

(A) 7 (B) 8 (C) 9 (D) 10

Answer:- (B)

Exp:- The expression can be written as

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )2 2 2 2 2 2 2 2

1 1 1 1.....

1 2 2 3 3 4 80 81

2 1 3 2 4 3 81 80.....

2 1 3 2 4 3 81 80

81 1 8

+ + + ++ + + +

− − − −= + + + +

− − − −

= − =

64. The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is

(A) 16,500 (B) 15,180 (C) 11,000 (D) 10,120

Answer:- (B)

Exp:- Let ‘W’ be the labour wages, and ‘T’ be the working hours.

Now, total cost is a function of W T×

Increase in wages = 20%

∴ Revised wages = 1.2 W



29

Decrease in labour time = 100

%24

1 23Re vised time 1 T T

24 24

23Re vised Total cos t 1.2 WT 1.15WT

24

1.15 13200 15180

∴ = − =

∴ = × =

= × =

65. After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history.

Which one of the following assertions is best supported by the above information?

(A) Failure is the pillar of success (B) Honesty is the best policy

(C) Life begins and ends with adventures (D) No adversity justifies giving up hope

Answer:- (D)

CS-GATE-2014 PAPER-01| www.gateforum.com


1


1. Which of the following options is the closest in meaning to the phrase underlined in the

sentence below?

It is fascinating to see life forms cope with varied environmental conditions.

(A) Adopt to (B) Adapt to (C) Adept in (D) Accept with

Answer: (B)

2. Choose the most appropriate word from the options given below to complete the following

sentence.

He could not understand the judges awarding her the first prize, because he thought that her

performance was quite ___________________.

(A) Superb (B) Medium (C) Mediocre (D) Exhilarating

Answer: (C)

3. In a press meet on the recent scam, the minister said, “The buck stops here”. What did the

minister convey by the statement?

(A) He wants all the money (B) He will return the money

(C) He will assume final responsibility (D) He will resist all enquiries

Answer: (C)

4. If ( ) ( )2 2 2z 1 / z 98, compute z 1 / z+ = +

Answer: (96)

Exp: Expanding

2 2

2 2

1 1 1z 2.z. 98 z 96

z z z+ + = ⇒ + =

5. The roots of 2ax bx c 0+ + = are real and positive a, b and c are real. Then 2ax b x c 0+ + =

has

(A) No roots (B) 2 real roots (C) 3 real roots (D) 4 real roots

Answer: (D)

Exp: ax2+bx+c=0

for roots to be real & +ve

b2-4ac>0

This will have 2 real positive roots.

2ax b x c 0+ + =

This can be written as;

2

2

ax bx c

Discri min ant b 4ac 0

+ +

= − >

2

2

2

ax bx c

( b) 4ac

b 4ac

− +

− −

⇒ −

Is also >0. This will have real roots

⇒ This will have 4 real roots.



2

Q.No. 6 – 10 Carry One Mark Each

6. The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the

Western Ghats in India, is lower than the hilly terrain to its north and south. The exact

reasons for the formation of this gap are not clear. It results in the neighbouring regions of

Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring

regions of Kerala having higher summer temperatures.

What can be inferred from this passage?

(A) The Palghat gap is caused by high rainfall and high temperatures in southern Tamil Nadu

and Kerala

(B) The regions in Tamil Nadu and Kerala that are near the Palghat Gap are low–lying

(C) The low terrain of the Palghat Gap has a significant impact on weather patterns in

neighbouring parts of Tamil Nadu and Kerala

(D) Higher summer temperatures result in higher rainfall near the Palghat Gap area

Answer: (C)

7. Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses

such as depression and schizophrenia, and consequently, that doctors will be able to eradicate

these diseases through early identification and gene therapy.

On which of the following assumptions does the statement above rely?

(A) Strategies are now available for eliminating psychiatric illnesses

(B) Certain psychiatric illnesses have a genetic basis

(C) All human diseases can be traced back to genes and how they are expressed

(D) In the future, genetics will become the only relevant field for identifying psychiatric

illnesses

Answer: (B)

8. Round–trip tickets to a tourist destination are eligible for a discount of 10% on the total fare.

In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single

person fare is Rs 100, a group of 5 tourists purchasing round–trip tickets will be charged Rs

___________

Answer: (850)

Exp: One way force =100

Two way fare per person=200

5 persons=1000/-

Total discount applicable=10+5=15%

15

Discount amount 1000 150100

= × =

Amount to be paid=1000-150=850



3

9. In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were

further asked to mention whether they own a car or scooter or both. Their responses are

tabulated below. What percent of respondents do not own a scooter?

Men Women

Own vehicle

Car 40 34

Scooter 30 20

Both 60 46

Do not own vehicle 20 50

Answer: (48)

Exp: Total respondents=300

Those who don’t have scooter

⇒ Men= 40+20=60

84Women 34 50

144

144% 100 48%

300

= + =

= × =

10. When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by

straight lines to its corners, how many (new) internal planes are created with these lines?

_______________________

Answer: (6)



4


1. Consider the statement:

“Not all that glitters is gold”

Predicate glitters (x) is true if x glitters and predicate gold (x) is true if x is gold. Which one

of the following logical formulae represents the above statement?

(A) ( ) ( )x; glitters x gold x∀ ⇒¬ (B) ( ) ( )x; gold x glitters x∀ ⇒

(C) ( ) ( )x; gold x glitters x∃ ∧ ¬ (D) ( ) ( )x; glitters x gold x∃ ∧ ¬

Answer: (D)

Exp: It means “It is false that every glitter is gold” or “some glitters are not gold”.

Then we can say “atleast one glitter object is not gold”.

2. Suppose you break a stick of unit length at a point chosen uniformly at random. Then the

expected length of the shorter stick is ________ .

Answer: (0.25)

Exp: The smaller sticks, therefore, will range in length from almost 0 meters up to a maximum of

0.5 meters, with each length equally possible.

Thus, the average length will be about 0.25 meters, or about a quarter of the stick.

3. Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then

which one of the following graphs has the same strongly connected components as G?

( ) ( ) ( ) ( ) 1 1 1A G V,E where E u,v | u,v E= = ∉

( ) ( ) ( ) ( ) 2 2 2B G V,E where E u,v | v,u E= = ∉

( ) ( ) ( ) 3 3 3C G V,E where E u,v | there is a path of length 2 from u to v in E= = ≤

( ) ( )4 4 4D G V ,E where V is the set of vertices in G which are not isolated=

Answer: (B)

Exp: Take an example for Graph G

. .

A B

Then option A and D will be eliminated.

Let G is below graph

Then G3 is a graph with below structure

In G the numbers of strongly connected components are 2 where as in G3 it is only one.

A B

A B



5

4 Consider the following system of equations:

3x 2y 1

4x 7z 1

x y z 3

x 2y 7z 0

+ =+ =

+ + =− + =

The number of solutions for this system is __________________

Answer: (1)

Exp: 3x 2y 1

4x 7z 1

x y z 3

x 2y 7z 0

+ =+ =

+ + =− + =

Augmented matrix is

3 2 0 1

4 0 7 1

1 1 1 3

1 2 7 0

−

1 3

1 1 1 3

4 0 7 1R R

3 2 0 1

1 2 7 0

↔ −

2 2 1 3 3 1 4 4 1

3 3 2

4 4 2

4 4 3

R R 4R R R 3R , R R R

1 1 1 3

0 4 3 11

0 1 3 8

0 3 6 3

1 1 1 3R 4R R

0 4 3 11

0 0 15 21R 4R 3R

0 0 15 21

1 1 1 3

0 4 3 11R R R

0 0 15 21

0 0 0 0

→ − → − → − − − − − − − −

→ − − −

− −→ −

− − → + − −

( ) ( )A : B A 3 no. of variables

Unique solution exists

ρ = ρ = =

∴

5. The value of the dot product of the eigenvectors corresponding to any pair of different eigen

values of a 4-by-4 symmetric positive definite matrix is ______________.

Answer: (0)



6

Exp: ( The eigen vectors corresponding to distinct eigen values of real symmetric matrix are

orthogonal)

6. Let the function

( ) ( ) ( ) ( )( ) ( ) ( )

sin cos tan

f sin cos tan6 6 6

sin cos tan3 3 3

θ θ θ

π π πθ =

π π π

Where ,6 2

π π θ =∈ and ( )f ' θ denote the derivative of f with respect to θ . Which of the

following statement is / are TRUE?

(I) There exists ,6 3

π π θ∈ such that ( )f ' 0θ = .

(II) There exists ,6 3

π π θ∈ such that ( )f ' 0θ ≠ .

(A) I only (B) II only (C) Both I and II (D) Neither I nor II

Answer: (C)

Exp: (By Mean value theorem)

7. Consider the following Boolean expression for F:

( )F P,Q,R,S PQ PQR PQRS= + +

The minimal sum-of products form of F is

( )A PQ QR QS+ + ( )B P Q R S+ + +

( )C P Q R S+ + + ( )D PR PRS P+ +

Answer: (A)

Exp: PQ PQR PQRS+ +

( )

( )( )( ) ( )( )

( )

( )( )

PQ PQ R RS

PQ PQ R R R S A BC A B A C

PQ PQ R S R R 1

Q P P R S

= + +

= + + + + = + +

= + + + =

= + +

∵

∵

( )( )( ) ( )( )

( )

Q P P P R S A BC A B A C

Q P R S P P 1

PQ QR QS

= + + + + = + +

= + + + =

= + +

∵

∵



7

8. The base (or radix) of the number system such that the following equation holds

is____________.

312

13.120

=

Answer: (5)

Exp: Let ‘x’ be the base or radix of the number system

( )

o 2o 1

o

2

2 2

2 2

2

2 x 1 x 3 x3 x 1 x 1 x

0 x 2 x

2 x 3x 13 x

2x x

3x x 2 3x x 1

2x x

3x x 2 6x 2x 2

x 5x 0

x x 5 0

x 0 or x 5

−× + × + ×= × + × + ×

× + ×

+ +⇒ = + +

+ + + +⇒ =

⇒ + + = + +

⇒ − =

⇒ − =

⇒ = =

As base or radix of a number system cannot be zero, here x 5=

9. A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of

which is 32 bits long. It needs to support 45 instructions, which have an immediate operand

in addition to two register operands. Assuming that the immediate operand is an unsigned

integer, the maximum value of the immediate operand is ____________.

Answer: (16383)

Exp: 1 Word 32 bits=

Each instruction has 32 bits

To support 45 instructions, opcode must contain 6-bits

Register operand1 requires 6 bits, since the total registers are 64.

Register operand 2 also requires 6 bits

14-bits are left over for immediate Operand Using 14-bits, we can give maximum 16383,

Since ( )142 16384 from 0 to 16383=

6 6 6 14

32 bits

opcode Reg opd 1 Reg opd 2immediate

opnd



8

10. Consider the following program in C language:

( )

( )( )

# include stdio.h

main

int i;

int * pi &i;

scanf "%d", pi ;

pr int f "%d \ n", i 5 ;

< >

=

+

Which one of the following statements is TRUE?

(A) Compilation fails.

(B) Execution results in a run-time error.

(C) On execution, the value printed is 5 more than the address of variable i.

(D) On execution, the value printed is 5 more than the integer value entered.

Answer: (D)

Exp: pi contains the address of i. So scanf("%d",pi) places the value entered in console into

variable i.e So printf("%d\n",i+5),prints 5 more than the value entered in console.

11. Let G be a graph with n vertices and m edges. What is the tightest upper bound on the

running time of Depth First Search on G, when G is represented as an adjacency matrix?

(A) (n)θ (B) ( )n mθ + (C) ( )2nθ (D) ( )2mθ

Answer: (C)

Exp: DFS visits each vertex once and as it visits each vertex, we need to find all of its neighbours

to figure out where to search next. Finding all its neighbours in an adjacency matrix requires

O(V ) time, so overall the running time will be O(V2).

12. Consider rooted n node binary tree represented using pointers. The best upper bound on the

time required to determine the number of sub trees having exactly 4 nodes is ( )a b0 n log n .

Then the value of a + 10b is_______

Answer: 1

Exp: int print_subtrees_size_4(node *n)

int size=0;

if(node==null)

return 0;

size=print_subtrees_size_4(node->left)+print_subtrees_size_4(node->right)+1;

if(size==4)

printf("this is a subtree of size 4");

return size;

The above function on taking input the root of a binary tree prints all the subtrees of size 4 in

O(n) time

so a=1 , b=0 and then a+10b=1



9

13. Consider the directed graph given below.


(A) The graph does not have any topological ordering

(B) Both PQRS and SRQP are topological orderings

(C) Both PSRQ and SPRQ are topological orderings.

(D) PSRQ is the only topological ordering.

Answer: (C)

Exp: Topological ordering of a directed graph is a linear ordering of its vertices such that for every

directed edge uv from vertex u to vertex v, u comes before v in the ordering. Topological

ordering is possible iff graph has no directed cycles.

(A) As the given graph doesn’t contain any directed cycles, it has at least one topological

ordering. So option (A) is false

(B) PQRS cannot be topological ordering because S should come before R in the ordering as

there is a directed edge from S to R.

SRQP cannot be topological ordering, because P should come before Q in the ordering as

there is a directed edge from P to Q

(C) PSRQ and SPRQ are topological orderings as both of then satisfy the above mentioned

topological ordering conditions.

(D) PSRQ is not the only one topological ordering as SPRQ is other possibility

14. Let P be a quick sort program to sort numbers in ascending order using the first element as

the pivot. Let t1 and t2 and t2 be the number of comparisons made by P for the inputs [1 2 3 4

5] and [4 1 5 3 2] respectively. Which one of the following holds?

(A) t1 =5 (B) t1 < t2 (C) t1>t2 (D) t1 = t2

Answer: (C)

Exp: Partition algorithm for quick sort

( ) [ ][ ] [ ]

[ ]

[ ] [ ][ ] [ ]

Partition A,P,q // A P,.....q

x A P // pivot A P

i P

for j P 1 to q

do if A j x

then i i 1

exchange A i A j

exchangeA P A i

← =←

= +≤← +

↔↔

return i [returning where pivot element is there after partitioning]

Recursively call the above algorithm for the two sub arrays [elements before and after pivot

element] to complete the sorting.

P Q

SR



10

x pivot

1 2 3 4 5

i j

=

2 1 ? NO≤

[ ]Pivot x A B

1 2 3 4 5

i j

= =

3 2 ? NO≤

1 2 3 4 5

i j

3 1 ? NO≤

1 2 3 4 5

i j

4 2 ? NO≤

1 2 3 4 5

i j

4 1 ? NO≤

1 2 3 4 5

i j

5 2 ? NO≤

1 2 3 4 5

i j

5 1 ? NO≤

[ ] [ ]exchange A P & A J

[ ] [ ]exchange A P & A i

[ ]x Pivot A P

1 2 3 4 5

i j

= =

4 3 ? NO≤

x Pivot

1 2 3 4 5

i j

=

5 4 ? NO≤

1 2 3 4 5

i j

5 3 ? NO≤



∴ Total 10 conparisons 1 2 3 4 5

Pivot ≥Pivot

1 2 3 4 5

Pivot ≥Pivot

1 2 3 4 5

Pivot ≥Pivot

Call recursively

for this

1 2 3 4 5

Pivot ≥PivotCall recursively

for this subarray



11

[ ]

[ ] [ ]

[ ] [ ]

x pivot A P

4 1 5 3 2

i j 1 4?Yes

i i 1 exchange A i & A j & increment j

4 1 5 3 2

i j 5 4?NO

4 1 5 3 2

i j 3 4?Yes

i i 1 exchange A i & A j & increment j

4 1 3 5 2

i J 2 4?Yes

= =

≤← +

≤

≤← +

≤

[ ] [ ]

i i 1

4 1 3 2 5

i j

exchange A P & A i

← +

( )

[ ] [ ]

x pivot A P

2 1 3 | 4 | 5

i j 1 2 ? yes

2 1 3 | 4 | 5

i j 3 2 ? NO

exchange A P & A i

= =

≤

≤

6 conparisons∴

15. Which one of the following is TRUE?

(A) The language L = n na b | n 0≥ is regular.

(B) The language L = na | n is prime is regular.

(C) The language L = w | w has 3k 1b's+ for some k ∈ N with a,bΣ = is regular.

(D) The language L = *ww | w with 0,1∈Σ Σ = is regular.

Answer: (C)

Exp: (A) n nL a b n 0= ≥ is a CFL but not regular, it requires memory for the representation

(B) nL a n is prime= is neither regular nor CFL

(C) L w | w has 3K 1 b 's for some k N with= + ∈

a,bΣ =

is a regular language, since the total count of b’s are multiple of 3 plus one. The regular

expression is ( ) ( )a * ba * a *ba *ba * ba * * a * ba * ba * ba * *a * ba *+

(D) L ww | w * with 0,1= ∈Σ Σ = is neither regular nor CFL

1 2 3 4 5

Pivot

2 1 3 4 5

Pivot≤Pivot ≥Pivot



12

16. Consider the finite automaton in the following figure.

What is the set of reachable states for the input string 0011?

(A) 0 1 2q ,q ,q (B) 0 1q ,q (C) 0 1 2 3q ,q ,q ,q (D) 3q

Answer: (A)

Exp: ( ) ( )0 0q ,0011 q ,011δ = δ

( ) ( )

( ) ( )

0

0 1

0 1

0 1 2

0 1 2

q ,11

q ,q ,1

q ,1 q ,1

q ,q q

q ,q ,q

= δ

= δ

= δ ∪ δ

= ∪

=


(A) A basic block is a sequence of instructions where control enters the sequence at the

beginning and exits at the end.

(B) Available expression analysis can be used for common subexpression elimination.

(C) Live variable analysis can be used for dead code elimination

(D) x 4*5 x 20= ⇒ = is an example of common subexpression elimination

Answer: (D)

Exp: x 4 5 x 20= × ⇒ = is not an example of common sub-expression but it is constant folding. In

constant folding expression consisting of constants will be replaced by their final value at

compile time, rather than doing the calculation in run-time.

18. Match the following

(1) Waterfall model (a) Specifications can be developed

(2) Evolutionary model (b) Requirements compromises are inevitable

(3) Component based software (c) Explicit recognition of risk

(4) Spiral development (d) Inflexible partitioning of the project into stages

(A) 1-a, 2-b, 3-c, 4-d (B) 1-d, 2-a, 3-b, 4-c

(C) 1-d, 2-b, 3-a, 4-c (D) 1-c, 2-a, 3-b, 4-d

Answer: (B)

Exp: The main drawback of the waterfall model is the difficulty of accommodating change after

the process is underway. One phase has to be complete before moving onto the next phase.

Inflexible partitioning of the project into distinct stages in waterfall model makes it difficult

to respond to changing customer requirements.

Evolutionary software models are iterative. They are characterized in manner that enables the

software engineers to develop increasingly more complete version of software.

In Spiral model, Development can be divided in to smaller parts and more risky parts can be

developed earlier which helps better risk management.

0,1

0q

1q

2q

3q0,10,11

1



13

19. Suppose a disk has 201 cylinders, numbered from 0 to 200. At some time the disk arm is at

cylinder 100, and there is a queue of disk access requests for cylinders 30, 85, 90, 100, 105,

110, 135 and 145. If Shortest-Seek Time First (SSTF) is being used for scheduling the disk

access, the request for cylinder 90 is serviced after servicing ____________ number of

requests.

Answer: (3)

Exp:

Request for cylinder is served after serving 3 requests ( )100,105 and 110


(A) User level threads are not scheduled by the kernel.

(B) When a user level thread is blocked, all other threads of its process are blocked.

(C) Context switching between user level threads is faster than context switching between

kernel level threads.

(D) Kernel level threads cannot share the code segment.

Answer: (D)

Exp: User threads are supported above the kernel and a managed without kernel support. The

thread function library to implement user level threads usually runs on top of the system in

user mode. Thus these threads with in a process are invisible to the operating system. Since

the kernel is unaware of the existence of such threads; when one user level thread is blocked

in the kernel all other threads of its process are blocked. So options (A) and (B) are true

(C) The OS is aware of kernel level threads. Kernel threads are scheduled by the OS’s

scheduling algorithms and require a “lightweight” context switch to switch between

(that is, registers, PC and SP must be changed, but the memory context remains the same

among kernel threads in the (same process). User level threads are much faster to switch

between as there is not context switch

(D) False

Kernel level threads within the same process share code section, data section and other

operating system resources such as open files and signals.

100

105

110

90

85

135145

30



14

21. Consider the relation scheme R = (E, F, G, H, I, J, K, L, M, N) and the set of functional

dependencies E,F→ G,F → ( )I,J , E,H K,L M→ → , K M ,→

L N→ on R. What is the key for R?

(A) E, F (B) E, F, H (C) E, F, H, K, L (D) E

Answer: (B)

Exp: ( )R EFGHI,JKLMN

F

EF G

F IJ

EH KL

K M

L

=

→

→

→

→

→ Ν

( )EF EFGIJ, E & F+ = Together functionally derive GIJ and if we observe given FDs, H

can’t be determined by any other attributes. So H must be part of all the (candidate) keys. H

along with E determines K and L, K & L functionally determine M and N respectively.

( )EFH EFGIJHKLMN+∴ =

∴ EFH is the only candidate for key.

22. Given the following statements:

S1: A foreign key declaration can always be replaced by an equivalent check

assertion in SQL

S2: Given the table R(a,b,c) where a and b together form the primary key, the following is a

valid table definition.

CREATE TABLE S (

a INTEGER,

d INTEGER,

e INTEGER,

PRIMARY KEY (d),

FOREIGN KEY (a) references R)

Which one of the following statements is CORRECT?

(A) S1 is TRUE and S2 is a FALSE (B) Both S1 and S2 are TRUE

(C) S1 is FALSE and S2 is a TRUE (D) Both S1 and S2 are FALSE



15

Answer: (D)

Exp: S1: Manager (Name, DeptID)

Department (DeptName, Deptid)

In given relation Manager DeptID is a foreign key referencing Deptid (P.K) of relation

Department.

Let’s declare the foreign key by an equivalent check assertion as follows:-

CREATE TABLE Manager (

Name Varchar (10)

DeptID INT (6) check (DeptID IN ( select Deptid from Department)),

PRIMARY KEY (Name)

);

The above use of check assertion is good to declare the foreign key as far as insertion is

considered for relation manager (will not insert any tuple in Manager containing such DeptID

value which is not present in any tuple of Department).

But the above declaration will fail to implement changes done in Department relation in

terms of deletion & updation. For an instance if a deptid present in Department gets deleted,

then respective reference in Manager should also be deleted.

∴ S1 is false.

S2: The given table definition is not valid due to invalid foreign key declaration. Attribute a

is declared as foreign key which is a single valued attribute and it is referencing the primary

key (ab) of relation R (a, b, c), which is a composite key.

A single value attribute cannot refer a composite key.

4 S2 is false.

23. Consider the following three statements about link state and distance vector routing protocols,

for a large network with 500 network nodes and 4000 links

[S1] The computational overhead in link state protocols is higher than in distance vector

protocols.

[S2] A distance vector protocol (with split horizon) avoids persistent routing loops, but not

a link state protocol.

[S3] After a topology change, a link state protocol will converge faster than a distance

vector protocol.

Which one of the following is correct about S1, S2, and S3?

(A) S1, S2, and S3 are all true (B) S1, S2, and S3 are all false.

(C) S1 and S2 are true, but S3 is false (D) S1 and S3 are true, but S2 is false.

Answer: (D)

Exp: Statement S1

The Distance Vector routing protocols rely on the information from their directly connected

neighbours in order to calculate and accumulate route information. Distance Vector routing

protocols require very little overhead as compared to Link State routing protocols as

measured by memory and processor power while the Link State routing protocols do not rely

solely on the information from the neighbours or adjacent router in order to calculate route

information. Instead, Link State routing protocols have a system of databases that they use in

order to calculate the best route to destinations in the network. This is TRUE



16

Statement S3

Distance Vector exchanges the routing updates periodically whether the topology is change

or not, this will maximize the convergence time which increases the chance of routing loops

while the Link State routing protocols send triggered change based updates when there is a

topology change. After initial flood, pass small event based triggered link state updates to all

other routers. This will minimize the convergence time that’s why there is no chance of

routing loops. This is TRUE.

24. Which one of the following are used to generate a message digest by the network security

protocols?

(P) RSA (Q) SHA-1 (R) DES (S) MD5

(A) P and R only (B) Q and R only (C) Q and S only (D) R and S only

Answer: (C)

Exp: RSA and DES are for Encryption where MD5 and SHA – 1 are used to generate Message

Digest.

25. Identify the correct order in which the following actions take place in an interaction between

a web browser and a web server.

1. The web browser requests a webpage using HTTP.

2. The web browser establishes a TCP connection with the web server.

3. The web server sends the requested webpage using HTTP.

4. The web browser resolves the domain name using DNS.

(A) 4,2,1,3 (B) 1,2,3,4 (C) 4,1,2,3 (D) 2,4,1,3

Answer: (A)

Exp: First of all the browser must now know what IP to connect to. For this purpose browser takes

help of Domain name system (DNS) servers which are used for resolving hostnames to IP

addresses. As browser is an HTTP client and as HTTP is based on the TCP/IP protocols, first

it establishes a TCP connection with the web server and requests a webpage using HTTP, and

then the web server sends the requested webpage using HTTP. Hence the order is 4,2,1,3

Q.No. 26 – 55 Carry Two Marks

26. Consider a token ring network with a length of 2km having 10 stations including a

monitoring station. The propagation speed of the signal is 2 x 108 m/s and the token

transmission time is ignored. If each station is allowed to hold the token for 2 µsec, the

minimum time for which the monitoring station should wait (in µsec) before assuming that

the token is lost is _______.

Answer: (28µs to 30µs)

Exp: Given Length (d) = 2 Km

No. of Stations (m) = 10

Propagation Speed (v) = 2 × 108 m/s

THT = 2µs

So, Max. TRT = TP in the Ring + No. of Active Stations * THT

= 10 × 10-6

+ 10 × 2 × 10-6

= 30 µs



17

27. Let the size of congestion window of a TCP connection be 32 KB when a timeout occurs.

The round trip time of the connection is 100 msec and the maximum segment size used is

2kB. The time taken (in msec) by the TCP connection to get back to 32KB congestion

window is ______

Answer: (1100 to 1300)

Exp: Given that at the time of Time Out, Congestion Window Size is 32KB and RTT = 100ms

When Time Out occurs, for the next round of Slow Start, Threshold = (size of Cwnd) / 2

It means Threshold = 16KB

Slow Start

2KB

1RTT

4KB

2RTT

8KB

3RTT

16KB ----------- Threshold reaches. So Additive Increase Starts

4RTT

18KB

5RTT

20KB

6RTT

22KB

7RTT

24KB

8RTT

26KB

9RTT

28KB

10RTT

30KB

11RTT

32KB

So, Total no. of RTTs = 11 → 11 * 100 = 1100

28. Consider a selective repeat sliding window protocol that uses a frame size of 1 KB to send

data on a 1.5 Mbps link with a one-way latency of 50 msec. To achieve a link utilization of

60%, the minimum number of bits required to represent the sequence number field is

________.



18

Answer: (5)

Exp:

p

Given L 1KB

B 1.5Mbps

T 50ms

60%

===

η =

Efficiency formula for SR protocol is

p

x

TW 60 Wa

1 2a 100 1 2a T

η = ⇒ = = + +

∵

3

x 6

L 8 10T 5.3ms

B 1.5 10

×= = =

×

p

x

T 50 500a 9.43

T 5.3 53= = = =

60 WW 11.9 12

100 19.86⇒ = ⇒ = ≈

n 1 n n 5W 2 12 2 24 2 24 2 n 5

−⇒ = = ⇒ = ⇒ = ≈ ⇒ =

29. Consider the following four schedules due to three transactions (indicted by the subscript)

using read and write on a data item x, denoted r (x) and w (x) respectively. Which one of

them is conflict serializable?

(A) r1 (x) ; r2 (x) ; w1 (x) ; r3(x) ; w2 (x) (B) r2 (x) ; r1 (x) ; w2 (x) ; r3(x) ; w1 (x)

(C) r3 (x) ; r2 (x) ; r1 (x) ; w2(x) ; w1 (x) (D) r2 (x) ; w2 (x) ; r3 (x) ; r1(x) ; w1 (x)

Answer: (D)

Exp: If there is a cycle in precedence graph, then the schedule is not conflict serializable.

(A) (B)

Not conflict serializable not conflict serializable

(C) (D)

Not conflict serializable it is conflict equivalent to

2 3 1

3 2 1

T T T &

T T T

→ →→ →

1T

2T

3T

1T

2T

3T

2T

3T

1T1

T2T

3T

1T

2T

3T



19

30. Given the following two statements:

S1: Every table with two single-valued attributes is in 1NF, 2NF, 3NF and BCNF

S2 : AB C, D E, E C→ → → is a minimal cover for the set of functional

dependencies AB C, D E, AB E,E C→ → → →

Which one of the following is CORRECT?

(A) S1 is TRUE and S2 is FALSE. (B) Both S1 and S2 are TRUE.

(C) S1 is FALSE and S2 is TRUE. (D) Both S1 and S2 are FALSE.

Answer: (A)

Exp: 1S : True

Consider any table R with two attributes ( )R A.B

The possible FD sets are

1F

A B

Key : A and is in BCNF

=→

2F

B A

Key : B and is in BCNF

=→

3F

A B

B A

Key : A & B It is in BCNF

=→→

4F

Key : AB and is in BCNF

=

If a table is in BCNF it is also in 1NF, 2NF and 3NF also

2S : False

First FD set cannot cover second FD set because in second FD set AB can functionally derive

E but that is not happing in first FD set.

31. An operating system uses the Banker’s algorithm for deadlock avoidance when managing the

allocation of three resource types X, Y, and Z to three processes P0, P1, and P2. The table

given below presents the current system state. Here, the Allocation matrix shows the current

number of resources of each type allocated to each process and the Max matrix shows the

maximum number of resources of each type required by each process during its execution.

There are 3 units of type X, 2 units of type Y and 2 units of type Z still available. The system

is currently in a safe state. Consider the following independent requests for additional

resources in the current state:

REQ1: P0 requests 0 units of X, 0 units of Y and 2 units of Z

REQ2: P1 requests 2 units of X, 0 units of Y and 0 units of Z

Allocation Max

X Y Z

0 0 1

3 2 0

2 1 1

X Y Z

8 4 3

6 2 0

3 3 3

P0

P1

P2



20


(A) Only REQ1 can be permitted.

(B) Only REQ2 can be permitted.

(C) Both REQ1 and REQ2 can be permitted.

(D) Neither REQ1 nor REQ2 can be permitted.

Answer: (B)

Exp: REQ1

Once 0P is allocated with ( )0,0,2 , the status of the system will be as follows

Allocation Max Need Available

X Y Z

0 0 3

3 2 0

2 1 1

X Y Z

8 4 3

6 2 0

3 3 3

X Y Z

8 4 0

3 0 0

1 2 2

X Y Z

3 2 0

With available ( ) 13,2,0 only P can be served. Once 1P is executed, available will be ( )6,4,0 ,

with ( )6,4,0 we can’t serve either 0 2P or P . Hence there is no safe sequence. Hence REQ1

can’t be permitted.

REQ2

Once 1P is allocated with ( )2,0,0 , the status of the system will be as follows

Allocated Max Need Available

0

1

2

P

P

P

X Y Z

0 0 1

5 2 0

2 1 1

X Y Z

8 4 3

6 2 0

3 3 3

X Y Z

8 4 2

1 0 0

1 2 2

X Y Z

1 2 2

With available ( )1,2,2 , we can serve either1 2P or P .

If we serve 1P then the safe sequence is 1 2 0P ,P ,P . If we serve

2P then the safe sequence is

2 1 0P ,P ,P . As true is at least one safe sequence we can permit REQ2.

32. Consider the following set of processes that need to be scheduled on a single CPU. All the

times are given in milliseconds

Process Name Arrival Time Execution Time

A 0 6

B 3 2

C 5 4

D 7 6

E 10 3

Using the shortest remaining time first scheduling algorithm, the average process turnaround

time (in msec) is ____________________.



21

Answer: (7.2)

Exp:

A B A C E D

0 3 5 8 12 15 21

( ) ( ) ( ) ( ) ( )8 0 5 3 12 5 21 7 15 10Average turn around time

5

367.2ms

5

− + − + − + − + −=

= ⇒

33. Assume that there are 3 page frames which are initially empty. If the page reference string 1,

2, 3, 4, 2, 1, 5, 3, 2, 4, 6, the number of page faults using the optimal replacement policy is

___________

Answer: (7)

Exp:

1 2 3 4 2 1 5 3 2 4

3 4 4 4 4 4 4 4 4

2 2 2 2 2 2 2 2 2 6

1 1 1 1 1 1 5 3 3 3 3

F F F F H H F F H H F

7 page faults

34. A canonical set of items is given below

s L. R

Q R.

→ >→

On input symbol < the set has

(A) a shift-reduce conflict and a reduce-reduce conflict.

(B) a shift-reduce conflict but not a reduce-reduce conflict.

(C) a reduce-reduce conflict but not a shift-reduce conflict.

(D) neither a shift-reduce nor a reduce-reduce conflict.

Answer: (D)

Exp:

>

From above diagram, we can see that there is no shift- reduce or reduce-reduce conflict.

→ >→

S L . R

Q R.→ >S L . R

oldI new

I



22

35. Let L be a language and L be its complement. Which of the following is NOT a viable

possibility?

(A) Neither L nor L is recursively enumerable (r.e.).

(B) One of L and L is r.e. but not recursive; the other is not r.e.

(C) Both L and L are r.e. but not recursive.

(D) Both L and L are recursive.

Answer: (C)

Exp: Recursive languages are closed under complement.

If a language L is recursive enumerable but not recursive then its complement is not a

recursive enumerable, so both L and L are recursive enumerable but not recursive is not a

viable possibility.

36. Which of the regular expressions given below represent the following DFA?

I) 0*1(1+00*1)*

II) 0*1*1+11*0*1

III) (0+1)*1

(A) I and II only (B) I and III only

(C) II and III only (D) I, II, and III

Answer: (B)

Exp: Given DFA will accept all the strings over 0,1ε = which are ending with 1.

( ) ( )0*1 1 00*1 * and 0 1 *1,+ + are the regular expressions for ending with 1.

37. There are 5 bags labelled 1 to 5. All the coins in a given bag have the same weight. Some

bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16

coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product

of the labels of the bags having 11 gm coins is ___.

Answer: 12

Exp: Let the weight of coins in the respective bags (1 through 5) be a,b,c,d and e-each of which

can take one of two values namely 10 or 11 (gm).

Now, the given information on total weight can be expressed as the following equation:

1.a+2.b+4.c+8.d+16.e = 323

⇒ a must be odd ⇒ a = 11

The equation then becomes:

11+2.b+4.c+8.d+16.e = 323

00 1

1



23

⇒ 2.b+4.c+8.d+16.e = 312

⇒ b+2.c+4.d+8.e = 156

⇒ b must be even ⇒ b = 10

The equation then becomes:

10+2.c+4.d+8.e = 156

⇒ 2.c+4.d+8.e = 146

⇒ c+2.d+4.e = 73

⇒ c must be odd ⇒ c = 11

The equation now becomes:

11+2.d+4.e = 73

⇒ 2.d+4.e = 62

⇒ d+2.e = 31

⇒ e = 11 and e = 10

Therefore, bags labelled 1, 3 and 4 contain 11 gm coins ⇒ Required Product = 1*3*4* = 12.

38. Suppose a polynomial time algorithm is discovered that correctly computes the largest clique

in a given graph. In this scenario, which one of the following represents the correct Venn

diagram of the complexity classes P, NP and NP Complete (NPC)?

Answer: (D)

Exp: The most important open question in complexity theory is whether the P = NP , which asks

whether polynomial time algorithms actually exist for NP-complete and all NP problems (

since a problem “C” is in NP-complete, iff C is in NP and every problem in NP is reducible

to C in polynomial time). In the given question it is given that some polynomial time

algorithm exists which computes the largest clique problem in the given graph which is

known NP-complete problem. Hence P=NP=NP-Complete.

( )A

P

NPC

NP

( )BP NP

NPC

( )B

NPC P NP=

( )D

P NP NPC= =



24

39. The minimum number of comparisons required to find the minimum and the maximum of

100 numbers is _________________.

Answer: (148)

Exp: From the list of given n numbers [say n is even],

Pick up first two elements, compare them

assign Current min min of two numbers

Current max max of two numbers

− =

− =

From the remaining n 2− numbers, take pairs wise and follow this process given below.

1. Compare two elements

Assign min = min of two numbers

max = max of two numbers

2. Compare min and current - min

Assign current min min current min,min− = −

3. Compare max and current - max

Assign current max max current max,max− = −

Repeat above procedure for all the remaining pairs of numbers. We can observe that each of

pair requires 3 comparisons

1. for finding min and max

2. For updating current – min

3. for updating current – max

But for initial pair we need only one comparison not 3.

( )3 n 2 3n 3n

total number of comparisons 1 3 1 22 2 2

−∴ = + = − + = −

Here n 100,= so number of comparisons = 148.

40. Consider a hash table with 9 slots. The hash function is ( )h k k mod 9.= The collisions are

resolved by chaining. The following 9 keys are inserted in the order: 5, 28, 19, 15, 20, 33, 12,

17, 10. The maximum, minimum, and average chain lengths in the hash table, respectively,

are

(A) 3, 0, and 1 (B) 3, 3, and 3 (C) 4, 0, and 1 (D) 3, 0, and 2



25

Answer: (A)

Exp:

Maximum & minimum chain lengths are 3 & 0 respectively

0 3 1 1 0 1 2 0 1Average chain length 1

9

∴+ + + + + + + +

= =

41. Consider the following C function in which size is the number of elements in the array E:

int MyX(int *E, unsigned int size)

int Y = 0;

int Z;

int i, j, k;

for(i = 0; i < size; i++)

Y = Y + E[i];

for(i = 0; i < size; i++)

for(j = i; j < size; j++)

Z = 0;

for(k = i; k <= j; k++)

Z = Z + E[k];

if (Z > Y)

Y = Z;

return Y;

The value returned by the function MyX is the

(A) maximum possible sum of elements in any sub-array of array E.

(B) maximum element in any sub-array of array E.

(C) sum of the maximum elements in all possible sub-arrays of array E.

(D) the sum of all the elements in the array E.

Answer: (A)

0

1

2

3

4

5

6

7

8

28 19 10

20

12

5

15 33

17



26

Exp: ( )int Myx int * E, unsin ged int sixe

( )[ ]

( )( )

( )[ ]

int Y 0;

int z;

int i, j,k;

for i 0;i size;i Calculates sum of the elements

of the array E and stores it in YY Y E i

for i 0; i size; i

for j i; j size; j

calculates the sum of elements o

z 0;

for k i;k j; k

z z E k ;

=

= < + +

= +

= < + +

= < + + = = <= + += +

( )

f

all posible subarrays of E

if z Y Checks whether sum of elements of each subarray

Y z; is greaer than the sum of elements of array if so, that sum

is assigned to Y, if not 'Y ' will be the sum of elements of

return Y; complete array

> →

=

Ultimately returns the maximum possible sum of elements in any sub array of given array E.

42. Consider the following pseudo code. What is the total number of multiplications to be

performed?

D= 2

for i = 1 to n do

for j = i to n do

for k = j + 1 to n do

D = D * 3

(A) Half of the product of the 3 consecutive integers

(B) One-third of the product of the 3 consecutive integers.

(C) One-sixth of the product of the 3 consecutive integers.


Answer: (C)



27

Exp:

( )

i 1, j 1, k 2 to n n 1 times

i 1, j 2, k 3 to n n 2 times

i 1, j 3, k 4 to n n 3 timesn 1 times

:

i 1, j n 2, k n 1 to n 2 times

i 1, j n 1, k n to n 1 time

= = = ⇒ −

= = = ⇒ − = = = ⇒ − ∑ −= = − = − ⇒

= = − = ⇒

( )

i 2, j 2,k 3 to n n 2 times

i 2, j 3,k 4 to n n 3 times

: : n 2 times

: :

i 2, j n 1,k n to n 1 time

:

:

i n 1, j n 1,k n to n 1 time 1 times

= = = ⇒ − = = = ⇒ − ∑ −

= = − = ⇒

= − = − = ⇒ ∑

( )( ) ( ) ( )

( )

( )( ) ( ) ( )( )( )

12 3 n 1

SS S S

n 1

i

i 1

2

Total number of multiplications

1 2 3 ...... n 1

1 1 2 1 2 3 .... 1 2 3 ..n 1

n n 1S

2

1 1n n

2 2

n n 1 2n 1 n n 1 n 1 n n 11 1

2 6 2 2 6

−

↓ ↓ ↓ ↓

−

=

∴

⇒∑ + ∑ + ∑ + ∑ −

= + + + + + + + + + + −

−= = ∑

= ∑ − ∑

+ + + − += − =

∑

43. Consider a 6-stage instruction pipeline, where all stages are perfectly balanced. Assume that

there is no cycle-time overhead of pipelining. When an application is executing on this 6-

stage pipeline, the speedup achieved with respect to non-pipelined execution if 25% of the

instructions incur 2 pipeline stall cycles is ______________________.

Answer: (4)

Exp: For 6 stages, non- pipelining takes 6 cycles.

There were 2 stall cycles for pipelining for 25% of the instructions

25So pipe line time 1 2

100

31.5

2

Non pipeline time 6Speed up 4

Pipeline time 1.5

= +

= =

−= = =



28

44. An access sequence of cache block addresses is of length N and contains n unique block

addresses. The number of unique block addresses between two consecutive accesses to the

same block address is bounded above K. What is the miss ratio if the access sequence is

passed through a cache of associativity A k≥ exercising least-recently-used replacement

policy?

(A) n/N (B) l/N (C) 1/A (D) k/n

Answer: (A)

45. Consider the 4-to-1 multiplexer with two lines S1 and S0 given below.

The minimal sum of-products form of the Boolean expression for the output F of the

multiplexer is

(A) PQ QR PQR+ + (B) PQ PQR PQR PQR+ + +

(C) PQR PQR QR PQR+ + + (D) PQR

Answer: (A)

Exp: PQ.O PQ.1 PQ.R PQR+ + +

PQ PQ.R PQR= + +

Hence the minimized expression is PQ QR PQR+ +

46. The function f(x) = x sin x satisfies the following equation. f"(x) + f(x) +tcosx = 0. The value

of t is______.

Answer: -2

Exp: ( ) ( )Given f " x f x t cos x 0+ + =

( )( )( ) ( )

( )( ) ( )

and f x xsin x

f ' x x cos x sin x

f " x x sin x cos x cos x

2cos x xsin x

2cos x f x

2cos x f x f x t cos x 0

2cos x t cos x t 2

=

= +

= − + +

= −

= −

∴ − + + =

⇒ =− ⇒ = −

0

1

R

R

0

1

2

31

s0

s

4 to 1

Multiplexer

− −F

QP

PQQR QR QR QR

1P

P

1

11QR

PQR



29

47. A function f(x) is continuous the interval [0,2]. It is known that f(0) = f(2) = -1 and f(1) = 1.

Which one of the following statements must be true?

(A) There exists a y in the interval (0,1) such that f(y) = f(y + 1)

(B) For every y in the interval (0,1), f(y) = f(2 - y)

(C) The maximum value of the function in the interval (0.2) is 1

(D) There exists a y in the interval (0,1) such that f(y) =f(2 – y)

Answer: (A)

Exp: Define g(x) =f(x)-f(x+1) in [0,1]. g(0) is negative and g(1) is positive. By intermediate value

theorem there is y€(0,1) such that g(y)=0

That is f(y) =f(y+1).

Thus answer is (a)

48. For fair six-sided dice are rolled. The probability that the sum of the results being 22is

X1296.

The value of X is _________

Answer: (10)

Exp: 22 occurred in following ways

6 6 6 4 4ways

6 6 5 5 6ways

→→

Required probability = 6 4 10

x 102296 2296

+= ⇒ =

49. A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence

of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possible 1-

pennants is (1), the set of all possible 2-pennants is (2), (1,1)and the set of all 3-pennants

is (2,1), (1,1,1), (1,2). Note that the pennant (1,2) is not the same as the pennant (2,1). The

number of 10- pennants is ______________.

Answer: (89)

Exp: No twos: 1111111111⇒1 pennant

Single two: 211111111⇒9!/8!1! = 9 pennants

Two twos: 22111111⇒8!/6!.2! = 28

Three twos: 2221111⇒7!/3!.4! = 35

Four twos: 222211⇒6!/4!.2! = 15

Five twos: 22222⇒1

Total = 89 pennants.

50. Let S denote the set of all functions 4f : 0,1 0,1→ . Denote by N the number of functions

from S to the set 0,1. The value of log2 log2 N is______.

Answer: (16)

Exp: The number of functions from A to B where size of A = |A| and size of B = |B| is |B||A|

0,14 = 0,1X0,1X0,1X0,1 = 16

|S| = 216

N = 2|S|

loglog N = log log 2|S|

= log |S| = log 216

= 16



30

51. Consider an undirected graph G where self-loops are not allowed. The vertex set of G is i,

f): 1 ≤ i ≤ 12, 1 ≤ j ≤ 12. There is an edge between (a,b) and (c,d) if a c 1− ≤ and

b d 1− ≤ The number of edges in the graph is _____________.

Answer: (506)

Exp: The graph formed by the description contains 4 vertices of degree 3 and 40verices of degree 5

and 100 vertices of degree 8.

According to sum of the degrees theorem 4*3+40*5+100*8 = 2|E|

|E| = 1012/2 = 506

52. An ordered n-tuple (d1,d2,…,dn) with 1 2 nd d .... d≥ ≥ ≥ is called graphic if there exists a

simple undirected graph with n vertices having degrees 1 2 nd ,d ,...,d respectively. Which of

the following 6-tuples is NOT graphic?

(A) (1, 1, 1, 1, 1, 1) (B) (2, 2, 2, 2, 2, 2)

(C) (3, 3, 3, 1, 0, 0) (D) (3, 2, 1, 1, 1, 0)

Answer: (C)

Exp: According to havel-hakimi theorem

(1,1,1,1,1,1) is graphic iff<1,1,1,1,0> is graphic

(0,1,1,1,1) is graphic iff (0,1,1,0) is graphic

(0,0,1,1) is graphic iff (0,0,0) is graphic

Since (0,0,0) is graphic (1,1,1,1,1,1) is also graphic.

(The process is always finding maximum degree and removing it from degree sequence,

subtract 1 from each degree for d times from right to left where d is maximum degree)

(2,2,2,2,2,2) is graphic iff (2,2,22-1,2-1) = (2,2,2,1,1) is graphic.

(1,1,2,2,2) is graphic iff (1,1,1,1) is graphic.

(1,1,1,1) is graphic iff (0,1,1)

(0,1,1) is graphic iff (0,0) is graphic.

Since (0,0) is graphic (2,2,2,2,2,2) is also graphic.

Consider option C now.

(3,3,3,1,0,0)(0,0,1,3,3,3) is graphic iff (0,0,0,2,2) is graphic.

Note that before applying the havel-hakimi step degree sequence should be in non-increasing

order.

(0,0,0,2,2) is graphic iff (0,0,-1,1) is graphic.

Since (0,0,-1,1) is not graphic (3,3,3,1,0,0) is also not graphic.

53. Which one of the following propositional logic formulas is TRUE when exactly two of p, q,

and r are TRUE?

(A) ( )( ) ( )p q r V p q ~ r↔ ∧ ∧ ∧ (B) ( )( ) ( )~ p q r V p q ~ r↔ ∧ ∧ ∧

(C) ( )( ) ( )p q r V p q ~ r→ ∧ ∧ ∧ (D) ( )( ) ( )~ p q r p q ~ r↔ ∧ ∧ ∧ ∧



31

Answer: (B)

Exp: P = T q=F and r=T

Option A will become false.

Option C will become false.

Option D is always false.

54. Given the following schema:

employees(emp-id, first-name, last-name, hire-date,

dept-id, salary)

departments(dept-id, dept-name, manager-id, location-id)

You want to display the last names and hire dates of all latest hires in their respective

departments in the location ID 1700. You issue the following query:

SQL>SELECT last-name, hire-date

FROM employees

WHERE (dept-id, hire-date) IN

(SELECT dept-id, MAX(hire-date)

FROM employees JOIN departments USING(dept-id)

WHERE location-id = 1700

GROUP BY dept-id);

What is the outcome?

(A) It executes but does not give the correct result.

(B) It executes and gives the correct result.

(C) It generates an error because of pairwise comparison.

(D) It generates an error because the GROUP BY clause cannot be used with table joins in a

sub-query.

Answer: (B)

Exp: In the inner sub query, “employees” and “departments” tables are joined by “using” clause

(first Cartesian product of those two tables will be done and then and wherever these is a

match on the dept-ids that tuple will be filtered). After this, the tuples of the resultant table

will be filtered by using the condition “location-id=1700” and then will grouped on dept-

id(all the tuples having equal values under dept-id will come into one group). After grouping,

the columns dept-id in location-id 1700 and maximum of hire dates in that respective dept-id

will be selected. Format of the tuples in the resultant table will be dept-id in location-id 1700

along with the latest hire date in the respective dept (two columns). Outer query takes each

tuple from “employees” table and it will check whether dept-id and hire-date pair for this

tuple is contained in the table given by inner sub query. If this is the case it will display the

last-name of respective employee

IN operator compares one or multiple expressions on the left side of the operator to a set of

one or more values on the right side of the operator. When using multiple expressions (like 2

columns - pair wise comparison), the number and data types of expressions in the list must

match on both sides of the operator.



32

55. Consider two processors P1 and P2 executing the same instruction set. Assume that under

identical conditions, for the same input, a program running on P2 takes 25% less time but

incurs 20% more CPI (clock cycles per instruction) as compared to the program running on

P1. If the clock frequency of P1 is 1GHz, then the clock frequency of P2 (in GHz) is

_________.

Answer: (1.6)

Exp: 1 cycle time for 9

1

10p 1n.s

1GH= =

Assume 1p takes 5 cycles for a program then 2p takes 20% more, means, 6 cycles.

2p Takes 25% less time, means, if 1p takes 5 n.s, then 2p takes 3.75 n.s.

Assume 2p clock frequency is x GHz.

2p Taken 6 cycles, so 96 10

3.75, x 1.6x GH

×= =



1


1. Choose the most appropriate phrase from the options given below to complete the following

sentence.

India is a post-colonial country because

(A) it was a former British colony

(B) Indian Information Technology professionals have colonized the world

(C) India does not follow any colonial practices

(D) India has helped other countries gain freedom

Answer: (A)

2. Who ___________ was coming to see us this evening?

(A) you said (B) did you say (C) did you say that (D) had you said

Answer: (B)

3. Match the columns.

Column 1 Column 2

(1) eradicate (P) misrepresent

(2) distort (Q) soak completely

(3) saturate (R) use

(4) utilize (S) destroy utterly

(A) 1:S, 2:P, 3:Q, 4:R (B) 1:P, 2:Q, 3:R, 4:S

(C) 1:Q, 2:R, 3:S, 4:P (D) 1:S, 2:P, 3:R, 4:Q

Answer: (A)

4. What is the average of all multiples of 10 from 2 to 198?

(A) 90 (B) 100 (C) 110 (D) 120

Answer: (B)

Exp:

[ ]

10 190 200

20 1809

(200) 9 100: 1900100

: 19 19

90 110

100

+ →− → × +

⇒ = =−

5. The value of 12 12 12 ....+ + + is

(A) 3.464 (B) 3.932 (C) 4.000 (D) 4.444



2

Answer: (C)

Exp: let 12 12 12 .... y= + + + =

2

12 y y

12 y y

(y 4)(y 3) 0

y 4, y 3

⇒ + =

⇒ + =⇒ − + =⇒ = = −


6. The old city of Koenigsberg, which had a German majority population before World War 2,

is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory

and has a predominantly Russian population. It is bordered by the Baltic Sea on the north and

the countries of Poland to the south and west and Lithuania to the east respectively. Which of

the statements below can be inferred from this passage?

(A) Kaliningrad was historically Russian in its ethnic make up

(B) Kaliningrad is a part of Russia despite it not being contiguous with the rest of Russia

(C) Koenigsberg was renamed Kaliningrad, as that was its original Russian name

(D) Poland and Lithuania are on the route from Kaliningrad to the rest of Russia

Answer: (B)

7. The number of people diagnosed with dengue fever (contracted from the bite of a mosquito)

in north India is twice the number diagnosed last year. Municipal authorities have concluded

that measures to control the mosquito population have failed in this region.

Which one of the following statements, if true, does not contradict this conclusion?

(A) A high proportion of the affected population has returned from neighbouring countries

where dengue is prevalent

(B) More cases of dengue are now reported because of an increase in the Municipal Office’s

administrative efficiency

(C) Many more cases of dengue are being diagnosed this year since the introduction of a new

and effective diagnostic test

(D) The number of people with malarial fever (also contracted from mosquito bites) has

increased this year

Answer: (D)

8. If x is real and2

x 2x 3 11− + = , then possible values of 3 2x x x− + − include

(A) 2, 4 (B) 2, 14 (C) 4, 52 (D) 14, 52

Answer: (D)



3

Exp: 2x 2x 3 11− + =

(x 4)(x 2) 0 x 4,x 2⇒ − + = ⇒ = = −

3 2Values of x x x

For x 4

Value 52

for x 2

Value 14

− + −

==

= −=

9. The ratio of male to female students in a college for five years is plotted in the following line

graph. If the number of female students doubled in 2009, by what percent did the number of

male students increase in 2009?

Answer: (140)

Exp: m

3f

= m

2.5f

= m=2.5f

m'3

2f

m ' 6f

m ' m

m

3.5f% 100

2.5f

71.4

8

% 140%

=

=−

=

↑ = ×

= =

↑=

3.5

3

2.5

2

1.5

1

0.5

02008 2009 2010 2011 2012

Ra

tio

of

m

ale

to

fe

m

ale

stu

de

nts



4

10. At what time between 6 a.m. and 7 a.m will the minute hand and hour hand of a clock make

an angle closest to 60°?

(A) 6: 22 a. m. (B) 6:27 a.m. (C) 6: 38 a.m. (D) 6:45 a.m.

Answer: (A)

Exp: Angle by minute’s hand

60 min → 360 ο

360

1min 660

ο→ =

o8min 48→

oAngle 48→ with number ‘6’

Angle by hours hand

o60 min 30

3022 min 22

60

11

=

→ ×

=

Total Angle=48+11=59o.



5


1. The security system at an IT office is composed of 10 computers of which exactly four are

working. To check whether the system is functional, the officials inspect four of the

computers picked at random (without replacement). The system is deemed functional if at

least three of the four computers inspected are working. Let the probability that the system is

deemed functional be denoted by p Then 100p= _____________.

Answer: (11.85 - 11.95)

Exp: p= P [at least three computers are working]

= P (3 or 4 computers working)

( ) ( )3 1 4

4 4

C C C

C C

4 6 4 5

10 10 42

100 p 11.9.

×= + =

⇒ =

2. Each of the nine words in the sentence ”The quick brown fox jumps over the lazy og” is

written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the

pieces is drawn at random from the box. The expected length of the word drawn is

_____________. (The answer should be rounded to one decimal place.

Answer: (3.8889)

Exp: Given words are

THE, QUICK, BROWN, FOX, JUMPS, OVER, THE, LAXY, DOG

LET X be the random variable such that X =length of the word

The Length of the words THE, FOX, THE, DOG is 3

The Length of the words OVER, LAXY is 4

The length of the words QUICK, BROWN, JUMPS, is 5

The corresponding probabilities are given below

x 3 4 5

P(X) 4/9 2/9 3/9

Expected length of the word= ( )xp x∑4 2 3

3 4 5 3.88899 9 9

= + + =

3. The maximum number of edges in a bipartite graph on 12 vertices is

__________________________.

Answer: (36)

Exp: The number of edges in a bipartite graph on n-vertices is atmost 2n

4

The maximum number of edges in a bipartite graph on 12 –vertices is 2n 12 12

364 4

×= =



6

4. If the matrix A is such that

[ ]2

A 4 1 9 5

7

= −

Then the determinant of A is equal to ________.

Answer: (0)

Exp:

( )2 1

2 18 10

A 4 36 20

7 63 35

A 0 R 2R .

= − −

⇒ = = −∵

5. A non-zero polynomial f(x) of degree 3 has roots at x = 1,x = 2 and x = 3. Which one of the

following must be TRUE?

(A) f(0) f(4) < 0 (B) f(0) f(4) > 0

(C) f(0) + f(4) > 0 (D) f(0) + f(4) < 0

Answer: (A)

Exp: Since, the roots of f(x) = 0 i.e., x = 1, 2, 3 lies between 0 and 4 and f(x) is of degree 3

∴ f(0) and f(4) are of opposite signs

⇒ f(0).f(4)<0.

6. The dual of a Boolean function ( )1 2 n,F x ,x ,....,x ,., '+ , written as FD, is the same expression as

that of F with + and swapped. F is said to be self-dual if F = FD. The number of self-dual

functions with n Boolean variables is

(A) 2n

(B) 2n-1

(C) n22

(D)

n 122−

Answer: (D)

Exp: A function F is self dual if it has equal number of minterms and maxterms, also mutually

exclusive terms should not be included.

The number of mutually exclusive terms (pair wise) is n

n 122

2

−=

Number of functions possible by taking any of the one term from the above mentioned

mutually exclusive pair is n 122 .

−

=

7. Let nk 2= . A circuit is built by giving the output of an n-bit binary counter as input to an n-

to-2n bit decoder. This circuit is equivalent to a

(A) k-bit binary up counter. (B) k-bit binary down counter.

(C) k-bit ring counter. (D) k-bit Johnson counter.

Answer: (C)

Exp: In case of decoder output, single output will be 1 and remaining will be zero at a time. The

output that is high will give the count of the ring counter at that time.



7

8. Consider the equation (123)5 = (x8)y with x and y as unknown. The number of possible

solutions is _____ .

Answer: (3)

Exp : ( ) ( )5 y

123 x8=

Converting both sides to decimal:

25 10 3 xy 8

xy 8 38 xy 30

x 1, y 30

or , x 2, y 15 or, x 3, y 10

⇒ + + = +⇒ + = ⇒ =⇒ = =

= = = =

∴ Total number of solutions: 3

9. A 4-way set-associative cache memory unit with a capacity of 16 KB is built using a block

size of 8 words. The word length is 32 bits. The size of the physical address space is 4 GB.

The number of bits for the TAG field is _____

Answer: (20)

Exp: Physical address size = 32 bits

( )

( )

14

149

5

bits

97

5

Cache size 16k bytes 2 Bytes

block size 8 words 8 4 Byte 32 Bytes

where each word b Bytes

2No. of blocks 2

2

block offset 9

2No. of sets 2

4

set ofset 7 bits

Byte offset 8 4 Bytes 32 Byte 2 5 bits

TAG 32 7 5 20 bits

= == = × =

=

= =

=

= =

=

= × = = =

= − + =

10. Consider the function func shown below:

int func(int num)

int count = 0;

while (num)

count++;

num>>= 1;

return (count);

The value returned by func(435)is __________.

32 bits

20 7 5

TAG

TAGBYTE

OFFSET

TAG

SET

OFFSET



8

Answer: (9)

Exp: int func (int num)

int count = 0;

while (num) //After each right shift, checks whether the num value is not zero//

count ++;

num ≫= 1; //shifts all bits of num one slot to the right//

return(count);

Initially num = 110110011, count = 0

count = 1; num = 101100110 after 1st right shift

count =2; num = 011001100 after 2nd

right shift

:

:

Count = 9; num = 000000000 after 9th right shift.

After nine right shifts, num = 0; and while loop terminates count = 9 will be returned.

11. Suppose n and p are unsigned int variables in a C program. We wish to set p to n

3C . If n is

large, which one of the following statements is most likely to set p correctly?

(A) p = n * (n – 1) * (n-2) / 6; (B) p = n * (n – 1) / 2 * (n-2) / 3;

(C) p = n * (n – 1) / 3 * (n-2) / 2; (D) p = n * (n – 1) / 2 * (n-2) / 6.0;

Answer: (B)

Exp: ( )( )

3C

n n 1 n 2P n

6

− −= =

It we multiply n, (n-1), (n-2) at once, it might go beyond the range of unsigned integer

(resulting overflow). So options (A) and (D) are rested out. If n is even or odd n×(n-1)/2 will

always result in integer value (no possibility of truncation, so more accuracy) where as incase

of n*(n-1)/3, its not certain to get integer always (truncation possible, so less accuracy).

( ) ( )1 2p p

P n * n 1 2* n 2 3= − −

As P1 will be having no error, resultant p will be more accurate.

( ) ( )1 2p p

P n * n 1 3* n 2 2= − −

As there is a possibility of truncation in P1, there will be less accuracy in final result of P.



9

12. A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order

traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in

that order. The level-order traversal of the heap after the insertion of the elements is:

(A) 10, 8, 7, 3, 2, 1, 5 (B) 10, 8, 7, 2, 3, 1, 5

(C) 10, 8, 7, 1, 2, 3, 5 (D) 10, 8, 7, 5, 3, 2, 1

Answer: (A)

Exp: Initial max-heap is after inserting 1

After inserting 7

Hence level order traversal is 10, 8, 7, 3, 2, 1, 5

13. Which one of the following correctly determines the solution of the recurrence relation with

T(1) = 1?

( ) nT n 2T log n

2

= +

(A) ( )nθ (B) ( )nlog nθ (C) ( )2nθ (D) ( )log nθ

Answer: (A)

Exp: By Master’s theorem case (i) ( ) ( )T n is O n

( )Here a 2, b 2, f n log n= = =

( ) ( ) ( )( ) ( )

( ) ( ) ( )

a 2

b 2

a a

b b

a

b

a

b

log log 1

we can choose 0, in such a way that

f n O n log ; i.e., log n O n log

By master theorem, If f n O n log for some 0, then

T n n log n

−∈ −∈

−∈

= =∈>

= =

= ∈>

= θ = θ

10

8 5

3 2

10

8 5

3 2 1

10

8 5

3 2 1 7

10

8 7

3 2 1 5

⇒

Heapification is not

required as it satisfies

max-heap property



10

14. Consider the tree arcs of a BFS traversal from a source node W in an unweighted, connected,

undirected graph. The tree T formed by the tree arcs is a data structure for computing

(A) the shortest path between every pair of vertices.

(B) the shortest path from W to every vertex in the graph.

(C) the shortest paths from W to only those nodes that are leaves of T.

(D) the longest path in the graph.

Answer: (B)

Exp: One of the application of BFS algorithm is to find the shortest path between nodes u and v.

But in the given question the BFS algorithm starts from the source vertex w and we can find

the shortest path from w to every vertex of the graph

15. n n

1 2IfL a | n 0 and L b | n 0 ,= ≥ = ≥ Consider

(I) L1.L2 is a regular language

(II) L1.L2 = n na b | n 0≥


(A) Only (I) (B) Only (II)

(C) Both (I) and (II) (D) Neither (I) nor (II)

Answer: (A)

Exp:

L1.L2 is also regular since regular languages are closed under concatenation.

But L1.L2 is not n na b | n 0≥ because both the variable is independent in both languages.

16. Let m

A ≤ B denotes that language A is mapping reducible (also known as many-to-one

reducible) to language B. Which one of the following is FALSE?

(A) If m

A ≤ B and B is recursive then A is recursive.

(B) If m

A ≤ B and A is undecidable then B is undecidable.

(C) If m

A ≤ B and B is recursively enumerable then A is recursively enumerable.

(D) If m

A ≤ B and B is not recursively enumerable then A is not recursively enumerable.

Answer: (D)

Exp: A language A is mapping reducible to a language B, if there is a computable function

f : * *ε → ε where for every ( )w,w A f w B∈ ⇔ ∈

If A mB≤ and B is Turing recognizable then A is Turing recognizable.

If A mB≤ and B is not recursively enumerable then A is not recursively enumerable



11

17. Consider the grammar defined by the following production rules, with two operators and +

S T *P

T U | T * U

P Q P | Q

Q Id

U Id

→→→ +

→→


(A) + is left associative, while * is right associative

(B) + is right associative, while * is left associative

(C) Both + and * are right associative

(D) Both + and * are left associative

Answer: (B)

Exp: S T P→ ×

T U | T U

P Q P | Q

Q Id

U Id

→ ×→ +→→

As the production rule T T U→ × is defined as left recursive rule, so * is left associate

operator.

As the production rule P Q P→ + is defined as right recursive rule, so + is right associative

operator.

18. Which one of the following is NOT performed during compilation?

(A) Dynamic memory allocation (B) Type checking

(C) Symbol table management (D) Inline expansion

Answer: (A)

Exp: Symbol table management is done during compitation to store and retriew the information

about tokens. Type checking is one of the check performed during semantic analysis of

compitation.

Inline expansion is a compiler optimization that replaces a function call by the bodyof

respective function.

Dynamic memory allocation is when an executing pregoram request the oprating system to

give it a block of main memory, so ti is performed during sum time not during complete time.

Option (A) is answer

19. Which one of the following is TRUE?

(A) The requirements document also describes how the requirements that are listed in the

document are implemented efficiently.

(B) Consistency and completeness of functional requirements are always achieved in

practice.

(C) Prototyping is a method of requirements validation.

(D) Requirements review is carried out to find the errors in system design.

Answer: (C)



12

20. A FAT (file allocation table) based file system is being used and the total overhead of each

entry in the FAT is 4 bytes in size. Given a 100 x 106 bytes disk on which the file system is

stored and data block size is 103 bytes, the maximum size of a file that can be stored on this

disk in units of 106 bytes is ____________.

Answer: (99.55 to 99.65)

Exp: Number of entries in the FAT = Disk Capacity/Block size = 108/10

3 = 10

5

Total space consumed by FAT = 105 * 4 B = 0.4 * 10

6 B

Maximum size of file that can be stored = 100 * 106 – 0.4 * 10

6 = 99.6 * 10

6 B

Answer: 99.6

21. The maximum number of super keys for the relation schema R (E, F, G, H) with E as the key

is __________.

Answer: (8)

Exp: The maximum number of super keys for the relation schema ( )R E,F,G,H with E as the key

is 32 8= as any subset of non key attributes along with key attribute will form the super key

of R.

As we have 3 nonkey all (F, G and H) so subsets will be 32

22. Given an instance of the STUDENTS relation as shown below:

Student D StudentName Student Email Student Age CPI

2345 Shankar Shankar@math X 9.4

1287 Swati swati@ee 19 9.5

7853 Shankar Shankar@cse 19 9.4

9876 Swati swati@mech 18 9.3

8765 Ganesh ganesh@civil 19 8.7

For (StudentName, StudentAge) to be a key for this instance, the value X should NOT be

equal to____________.

Answer: (19)

Exp: For (Student Name, student age) to be a key for given instance of STUDENTS relation, the

pair value should not get repeated in any two tuples p and q (uniqueness in forced by the

definition of key)

Tuple Student Name Student Age

P Shankar should not be 19⊗ →

Q Shankar 19



13

23. Which one of the following is TRUE about the interior gateway routing protocols – Routing

Information Protocol (RIP) and Open Shortest Path First (OSPF)?

(A) RILP uses distance vector routing and OSPF uses link state routing

(B) OSPF uses distance vector routing and RIP uses link state routing

(C) Both RIP and OSPF use link state routing

(D) Both RIP and OSPF use distance vector routing

Answer: (A)

Exp: RIP Uses Distance Vector Routing and OSPF uses Link State Routing.

24. Which one of the following socket API functions converts an unconnected active TCP socket

into a passive socket?

(A) connect (B) bind (C) listen (D) accept

Answer: (C)

Exp:

(a) The connect function is used by a TCP client to establish a connection with a TCP

server.

(b) The bind function assigns a local protocol address to a socket. With the Internet

protocols, the protocol address is the combination of either a 32-bit IPv4 address or a

128-bit IPv6 address, along with a 16-bit TCP or UDP port number.

(c) The listen function converts an unconnected socket into a passive socket, indicating that

the kernel should accept incoming connection requests directed to this socket.

(d) The accept function is called by a TCP server to return the next completed connection

from the front of the completed connection queue. If the completed connection queue is

empty, the process is put to sleep (assuming the default of a blocking socket).

25. In the diagram shown below, L1 is an Ethernet LAN and L2 is a Token-Ring LAN. An IP

packet originates from sender S and traverses to R, as shown. The links within each ISP and

across the two ISPs, are all point-to-point’ optical links. The initial value of the TTL field is

32. The maximum possible value of the TTL field when R receives the datagram is

____________.

Answer: (26)

Exp:

ISP2

S LAN L1

ISP1

LAN L2

R

LAN L1S

ISP1

ISP1

RLAN L2



14

The TTL field is set by the sender of the datagram, and reduced by every router on the route

to its destination. So, there are 5visits at 5 routers and one visit at receiver R in above figure

which leads 32 – 6 = 26.


26. Consider the store and forward packet switched network given below. Assume that the

bandwidth of each link is 106 bytes / sec. A user on host A sends a file of size 10

3 bytes to

host B through routers R1 and R2 in three different ways. In the first case a single packet

containing the complete file is transmitted from A to B. In the second case, the file is split

into 10 equal parts, and these packets are transmitted from A to B. In the third case, the file is

split into 20 equal parts and these packets are sent from A to B. Each packet contains 100

bytes of header information along with the user data. Consider only transmission time and

ignore processing, queuing and propagation delays. Also assume that there are no errors

during transmission. Let T1, T2 and T3 be the times taken to transmit the file in the first,

second and third case respectively. Which one of the following is CORRECT?

(A) T1 < T2 < T3 (B) T1 > T2 > T3

(C) T2 = T3, T3 < T1 (D) T1 = T3, T3 > T2

Answer: (D)

Exp: Given Bandwidth = 106 bytes/sec

L=103 bytes

Case: 1

x 6

1

L 1000 bytes

Header size 100 bytes

Total Frame size 1000 100 1100 bytes

1100 8T 1100 s

10 8

So, T 3300 s

==

= + =×

∴ = = µ×

= µ

Case: 2

x 6

2

L 100 bytes



200 8T 200 s for 1 packet

10 8

For 10 packets Tx 2000 s

So, T 2000 200 200 2400 s

==

= + =×

∴ = = µ×

⇒ = µ= + + = µ

A R1 R2 B



15

Case: 3

x 6

3

L 50 bytes



150 8T 150 s for 1 packet

10 8

For 20 packets Tx 3000 s

So, T 3000 150 150 3300 s

=

=

= + =

×∴ = = µ

×

⇒ = µ

= + + = µ

∴ 1 3

3 2

T T

T T

=>

27. An IP machine Q has a path to another IP machine H via three IP routers R1, R2, and R3.

Q—R1—R2—R3—H

H acts as an HTTP server, and Q connects to H via HTTP and downloads a file. Session layer

encryption is used, with DES as the shared key encryption protocol. Consider the following

four pieces of information:

[I1] The URL of the file downloaded by Q

[I2] The TCP port numbers at Q and H

[I3] The IP addresses of Q and H

[I4] The link layer addresses of Q and H

Which of I1, I2, I3, and I4 can an intruder learn through sniffing at R2 alone?

(A) Only I1 and I2 (B) Only I1 (C) Only I2 and I3 (D) Only I3 and I4

Answer: (C)

Exp: An Intruder can’t learn [I1] through sniffing at R2 because URLs and Download are

functioned at Application layer of OSI Model.

An Intruder can learn [I2] through sniffing at R2 because Port Numbers are encapsulated in

the payload field of IP Datagram.

An Intruder can learn [I3] through sniffing at R2 because IP Addresses and Routers are

functioned at network layer of OSI Model.

An Intruder can’t learn [I4] through sniffing at R2 because it is related to Data Link Layer of

OSI Model.

28. A graphical HTML browser resident at a network client machine Q accesses a static HTML

webpage from a HTTP server S. The static HTML page has exactly one static embedded

image which is also at S. Assuming no caching, which one of the following is correct about

the HTML webpage loading (including the embedded image)?



16

(A) Q needs to send at least 2 HTTP requests to S, each necessarily in a separate TCP

connection to server S

(B) Q needs to send at least 2 HTTP requests to S, but a single TCP connection to server S is

sufficient

(C) A single HTTP request from Q to S is sufficient, and a single TCP connection between Q

and S is necessary for this

(D) A single HTTP request from Q to S is sufficient, and this is possible without any TCP

connection between Q and S

Answer: (B)

29. Consider the following schedule S of transactions T1, T2, T3, T4:

T1 T2 T3 T4

Writes [x]

Commit

Reads[X]

Writes[X]

Commit

Writes[Y]

Reads [Z]

Commit

Reads[X]

Reads[Y]

Commit

Which one of the following statements is CORRECT?

(A) S is conflict-serializable but not recoverable

(B) S is conflict-serializable but is recoverable

(C) S is both conflict-serializable and recoverable

(D) S is neither conflict-serializable nor is it recoverable

Answer: (C)

Exp: The precedence graph of schedule s is a follows.

In the schedule S of transactions 1 2 3 4T ,T ,T and T for each pair of transaction i jT and T , such

that jT reads a data item previously written by iT the commit operation of jT appears after

the commit operation of iT hence the schedule is recoverable schedule.

2T

3

1

4

T

T

T

⇒ No cycle, so S is conflict

serializable



17

30. Consider a join (relation algebra) between relations r(R)and s(S) using the nested loop

method. There are 3 buffers each of size equal to disk block size, out of which one buffer is

reserved for intermediate results. Assuming size(r(R))<size(s(S)), the join will have fewer

number of disk block accesses if

(A) relation r(R) is in the outer loop.

(B) relation s(S) is in the outer loop.

(C) join selection factor between r(R) and s(S) is more than 0.5.

(D) join selection factor between r(R) and s(S) is less than 0.5.

Answer: (A)

Exp: A join between r(R) and s (S) using nested loop method will be as follows.

For each tuple r in R do

For each tuple s in S do

If r and s satisfy the join condition then output the tuple <r,s>

This algorithm will involve nr*bs+br block transfers and nr+br seeks, where br and bs are

number of blocks in relations R and S respectively and nr is number of tuple in relation R.

Now to have less block accesses, nr should be less and it is already given that |R|<|S|. Relation

r(R) should be in the outer loop to have fewer number of disk block accesses.

31. Consider the procedure below for the Producer-Consumer problem which uses semaphores:

Semaphore n = 0;

Semaphore s = 1;

Void producer ( ) Void consumer( )

while (true) while(true)

Produce ( ); semWait (s) ;

SemWait (s); semWait (n) ;

addToBuffer ( ); removeFromBuffer ( ) ;

semSignal (s); semsignal (s);

semSignal (n); consume ( ) ;


(A) The producer will be able to add an item to the buffer, but the consumer can never

consume it.

(B) The consumer will remove no more than one item from the buffer.

(C) Deadlock occurs if the consumer succeeds in acquiring semaphore s when the buffer is

empty.

(D) The starting value for the semaphore n must be 1 and not 0 for deadlock-free operation.

Answer: (C)

Exp: (A) The producer will be able to add an item to the buffer, but the consumer can never

consume if given statement is false, because once producer produces an item and places

in buffer, the next turn to execute can be given to consumer ( ). [The value of s = 1 and

n=1]. So consumer will be definitely able to consume it by performing successful down

operations on s and n.



18

(B) The consumer will remove no more than one item from the buffer.

Given statement is false as if p( ) produces and adds to buffer, (c) will consume the

added item, this sequence of alteration (p and c) will always make consumer to remove

items from buffer.

This statement would have been true if it was said that the consumer will remove no more

than one item from the buffer one after the other. ( at a time).

(C) Dead lock occurs if the consumer succeeds in acquiring semaphore‘s’ when the buffer is

empty. Given statement is true as when buffer is empty initially if consumer gets the turn

to execute as follows:-

S = 1, n = 0;

( )

( )

( )( ) [ ]

consumer

while True

p s ; s 10

p s ; m 0; it blocksconsumer

=

=

( )

( )

( )( ) ( )

producer

while True

producer ;

p s ; s 0; it blocks p

=

So from the above execution both producer and consumer goes in block state waiting for each

other to wake them up and hence dead lock occurs.

(D) Even if the starting value for the semaphore ‘n’ becomes 1, there will be invalid

execution of consumer on buffer empty condition, which should not happen. So

statement is false.

32. Three processes A, B and C each execute a loop of 100 iterations. In each iteration of the

loop, a process performs a single computation that requires tc CPU milliseconds and then

initiates a single I/O operation that lasts for tio milliseconds. It is assumed that the computer

where the processes execute has sufficient number of I/O devices and the OS of the computer

assigns different I/O devices to each process. Also, the scheduling overhead of the OS is

negligible. The processes have the following characteristics:



19

Process id tc tio

A 100ms 500ms

B 350ms 500ms

C 200ms 500ms

The processes A, B, and C are started at times 0, 5 and 10 milliseconds respectively, in a pure

time sharing system (round robin scheduling) that uses a time slice of 50 milliseconds. The

time in milliseconds at which process C would complete its first I/O operation is

___________.

Answer: (1000)

Exp:

The Gantt chart for Round robin algorithm for the first iteration execution for each of the 3

processes is as follows:

R .Q A B C A

A B C A B C B C B C B

0 50 100 150 200 250 300 350 400 450 500 650

After finishing ct CPU ms at time 500ms, C goes for I/O operation, that needs 500ms more,

so the time at which process C would complete its first I/O operations is 500+500 = 1000ms

33. A computer has twenty physical page frames which contain pages numbered 101 through

120. Now a program accesses the pages numbered 1, 2, …, 100 in that order, and repeats the

access sequence THRICE. Which one of the following page replacement policies experiences

the same number of page faults as the optimal page replacement policy for this program?

(A) Least-recently-used (B) First-in-first-out

(C) Last-in-first-out (D) Most-recently-used

Answer: (D)

Exp: Page reference string for the program will be:-

1, 2, 3, 4, ------------100, 1, 2, 3, 4, ------------100, 1, 2, 3, 4, ------------100,

The current status of 20 frames shows page numbers from 101 to 120.

Implementation of optimal page replacement policy for above given page reference string

would be as follows:

Process id ct iot A.T TQ = 50ms

A

B

C

100 ms

350 ms

200 ms

500 ms

500 ms

500 ms

0 ms

5 ms

10 ms

A goesforI o operation

C goesforI o operation



20

0 101 1 40 41 80 81 20 21 60 61 100 1 40 41 80 81

1 102 2 39 42 79 82

2 103 3 38 43 78 83

3 104 4 37 44 77 84

4 105 5 36 45 76 85

5 106 6 35 46 75 86

6 107 7 34 47 74 87

7 108 8 33 48 73 88

8 109 9 32 49 72 89

9 110 10 31 50 71 90

10 111 11 30 51 70 91

11 112 12 29 52 69 92

12 113 13 28 53 68 93

13 114 14 27 54 67 94

14 115 15 26 55 66 95

15 116 16 25 56 65 96

16 117 17 24 57 64 97

17 118 18 23 58 63 98

18 119 19 22 59 62 99

19 120 20 21 60 61 100 1 40 41 80 81 20 21 60 61 100

↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓

20PF 20PF 20PF 20PF 20PF 20PF 20PF 20PF 20PF 20PF

So there would be 300 page faults in total (each access 100 page faults).

Also it is visible that every time a replacement is done for the page which is most recently

referred as it will be least recently referred in future. So for the given page reference string

optimal page replacement policy is working same as most recently used policy and thus

number of page faults will be same in both of them.

34. For a C program accessing X[i] [j] [k], the following intermediate code is generated by a

compiler. Assume that the size of an integer is 32 bits and the size of a character is 8 bits.

t0 = i * 1024

t1 = j * 32

t2 = k * 4

t3 = t1 + t0

t4 = t3 + t2

t5 = X[t4]

Which one of the following statements about the source code for the C program is

CORRECT?

st1 time access nd2 time access

rd3 time access



21

(A) X is declared as “int X[32] [32] [8]”.

(B) X is declared as “int X[4] [1024] [32]”.

(C) X is declared as “char X[4] [32] [8]”.

(D) X is declared as “char X[32] [16] [2]”.

Answer: (A)

Exp: It is given that Size of int is 4B and of char is 1B. The memory is byte addressable.

Let the array be declared as Type X[A][B][C] (where Type = int/char and A,B,C are natural

numbers).

From t0 = i*1024, we conclude that B*C*(size of Type) = 1024.

From t1 = j*32, we conclude that C*(size of Type) = 32.

From t2 = k*4, we conclude that size of Type = 4.

Type = int, and

C = 8, and

B = 32.

35. Let < M > be the encoding of a Turing machine as a string over 0,1Σ = . Let L = <M> |M

is a Turning machine that accepts a string of length 2014. Then, L is

(A) decidable and recursively enumerable

(B) undecidable but recursively enumerable

(C) undecidable and not recursively enumerable

(D) decidable but not recursively enumerable

Answer: (B)

Exp: The language accepted by the Turing machine is recursively enumerable. If is undecidable as

the Turing machine may halt or it may loop for the strings whose length is not equal to 2014.

36. Let 1L w 0,1 * |= ∈ w has at least as many occurrences of (110)’s as (011)’s. Let

2L w 0,1 * |= ∈ w has at least as many occurrence of (000)’s as (111)’s. Which one of the

following is TRUE?

(A) 1L is regular but not 2L (B) 2L is regular but not 1L

(C) Both 1L and 2L are regular (D) Neither 1L nor 2L are regular

Answer: (A)

Exp: The automaton for L1 is as follows:

No finite state automata can be constructed for L2.

10

0

0

0

0

0

0

1

0,1

1

1

1

11



22

37. Consider two strings A "q pqrr" and B "pqprqrp".= = Let x be the length of the longest

common subsequence (not necessarily contiguous) between A and B and let y be the number

of such longest common subsequences between A and B. Then x + 10y = ___.

Answer: (34)

Exp: Given is

A = “qpqrr” B = “pqprqrp”

The longest common subsequence (not necessarily contiguous) between A and B is having 4

as the length, so x=4 and such common subsequences are as follows:

(1) qpqr

(2) pqrr

(3) qprr

So y = 3 (the number of longest common subsequences) hence x+10y = 4+10*3 = 34.

38. Suppose P, Q, R, S, T are sorted sequences having lengths 20, 24, 30, 35, 50 respectively.

They are to be merged into a single sequence by merging together two sequences at a time.

The number of comparisons that will be needed in the worst case by the optimal algorithm for

doing this is ____.

Answer: (358)

Exp: The implementation of optimal algorithm for merging sequences is as follows.

In the above implementation, total number of comparisons is

(44-1)+(94-1)+(65-1)+(159-1) = 358

Hint: The number of comparisons for merging two sorted sequences of length m and n is

m+n-1.

39. Consider the expression tree shown. Each leaf represents a numerical value, which can either

be 0 or 1. Over all possible choices of the values at the leaves, the maximum possible value

of the expression represented by the tree is ___.

159

94

44 50

2420 30 35

65



23

Answer: (6)

Exp:

So as per the above tree where leaves have been given the values, the maximum possible

value of the expression represented by the tree is 6.

40. Consider the following function

double f (double x)

if ( abs (x*x – 3) < 0. 01) return x;

else return f (x / 2 + 1.5/x);

Give a value q (to 2 decimals) such that f (q) will return q:______

Answer: (1.72 to 1.74)

Exp: If condition given in function definition should be ‘TRUE’, for ( )f q to return value q.

The condition is as follows:

( )( )if abs x x 3 0.01 return x;× − <

The above condition will be true when x=1.73.

41. Suppose a stack implementation supports an instruction REVERSE, which reverses the order

of elements on the stack, in addition to the PUSH and POP instructions. Which one of the

following statements is TRUE with respect to this modified stack?

+

−

+ −

0 /1 0 /1 0 /1 0 /1 0 /1 0 /1 0 /1 0 /1

− +

+

+

+

+−−

−

+

1 1 0 1 1 1 10

3

2

6

2

3

1− 1



24

(A) A queue cannot be implemented using this stack.

(B) A queue can be implemented where ENQUEUE takes a single instruction and

DEQUEUE takes a sequence of two instructions.

(C) A queue can be implemented where ENQUEUE takes a sequence of three instructions

and DEQUEUE takes a single instruction.

(D) A queue can be implemented where both ENQUEUE and DEQUEUE take a single

instruction each.

Answer: (C)

Exp: Option (a) is false because queue can be implemented by using the modified stack as by

reversing the stack. LIFO will become FIFO.

Implementation of ENQUEUE & DEQUEUE takes four sequence of instructions as follows:

1. Enqueue: Reverse, Push, Revesre

Dequeue: POP

(OR)

2. Enqueue: Push

Dequeue: Reverse, POP, Reverse

42. Consider the C function given below

int f(int j)

static int i = 50;

int k;

if (i == j)

printf(“something”);

k = f(i);

return 0;

else return 0;


(A) The function returns 0 for all values of j.

(B) The function prints the string something for all values of j.

(C) The function returns 0 when j = 50.

(D) The function will exhaust the runtime stack or run into an infinite loop when j = 50.

Answer: (D)

Exp: For any value of ‘j’ other than 50 the function will return 0, for j=50, then condition (i==j)

will be true, it will print “something” and function will be called recursively with same value

till the run time stack overflows.



25

43. In designing a computer’s cache system, the cache block (or cache line) size is an important

Parameter. Which one of the following statements is correct in this context?

(A) A smaller block size implies better spatial locality

(B) A smaller block size implies a smaller cache tag and hence lower cache tag overhead

(C) A smaller block size implies a larger cache tag and hence lower cache hit time

(D) A smaller block size incurs a lower cache miss penalty

Answer: (D)

Exp: When a cache block size is smaller, it could accommodate more number of blocks, it

improves the hit ratio for cache, so the miss penalty for cache will be lowered.

44. If the associativity of a processor cache is doubled while keeping the capacity and block size

unchanged, which one of the following is guaranteed to be NOT affected?

(A) Width of tag comparator

(B) Width of set index decoder

(C) Width of way selection multiplexor

(D) Width of processor to main memory data bus

Answer: (D)

Exp: When associativity is doubled, then the set offset will be effected, accordingly, the number of

bits used for TAG comparator be effected.

Width of set index decoder also will be effected when set offset is changed.

Width of wag selection multiplexer wil be effected when the block offset is changed.

With of processor to main memory data bus is guaranteed to be NOT effected.

45. The value of a float type variable is represented using the single-precision 32-bit floating

point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23

bits for mantissa. A float type variable X is assigned the decimal value of −14.25. The

representation of X in hexadecimal notation is

(A) C1640000H (B) 416C0000H (C) 41640000H (D) C16C0000H

Answer: (A)

Exp: (A)

S E M

1 bit 8 bits 23 bits

( ) ( )

( ) ( )

10 2

0

3

10 2

14.25 1110.01

1110.01 2

1.11001 2

S:1

E : 3 127 10000010

M :11001000

=

×

= ×

+ =

− − − − −

Value stored:

H[C 1 6 4 0 0 0 0 ]

11 0 00 0 0 10 11 00 1 0 0 0 0 − − −



26

46. In the Newton-Raphson method, an initial guess of 0x 2= is made and the sequence

0 1 2x ,x ,x ... is obtained for the function

3 20.75x 2x 2x 4 0− − + =

Consider the statements

(I) 3x 0= .

(II) The method converges to a solution in a finite number of iterations.


(A) Only I (B) Only II (C) Both I and II (D) Neither I nor II

Answer: (A)

Exp: ( ) ( )3 2 2f x 0.75 x 2x 2x 4; f ' x 2.25x 4x 2= − − + = − −

0 0 0

01 0

0

1 1

12 1

1

2 2

23 2

2

x 2, f 2; f ' 1

fx x 0

f '

f 4; f ' 2

fx x 2

f '

f 2,f ' 1

fx x 0

f '

= = − = −

∴ = − =

⇒ = = −

∴ = − =

⇒ = − = −

∴ = − =

Also, root does not lies between 0 and 1.

So, the method diverges if x0 = 2

∴only (I) is true.

47. The product of the non-zero eigenvalues of the matrix

1 0 0 0 1

0 1 1 1 0

0 1 1 1 0

0 1 1 1 0

1 0 0 0 1

is_______.

Answer: (6)

Exp:

1 0 0 0 1

0 1 1 1 0

Let A 0 1 1 1 0

0 1 1 1 0

1 0 0 0 1

=



27

1

2

3

4

5

x

x

Let X x be eigen vector

x

x

=

By the definition of eigen vector, AX= λ X

1 1

2 2

3 3

4 4

5 5

x x1 0 0 0 1

x x0 1 1 1 0

x x0 1 1 1 0

x x0 1 1 1 0

x x1 0 0 0 1

= λ

1 5 5

2 3 4 2

2 3 4 3

2 3 4 4

1 5 4 1 5 5 4

x x x

x x x x

x x x x

x x x x

x x x x x x x

+ = λ

+ + = λ+ + = λ+ + = λ

+ = λ ⇒ + = λ = λ

2 3 4 2 3 4and x x x x x x+ + = λ = λ = λ

(1) If 0λ ≠ say 1 5x x a= =

2 3 4x x x b= = =

1 5

2 3 4

x x a 2a a 2

x x x a 3a a 3

⇒ + = λ ⇒ = λ ⇒ λ =

+ + = λ ⇒ = λ ⇒ λ =

(2) if 0λ = ⇒ eigen value =0

∴ Three distinct eigen values are 0,2,3 product of non zero eigen values =2×3=6

48. The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT

divisible by 2, 3 or 5 is ______ .

Answer: (0.259 to 0.261)

Exp: Let A = divisible by 2, B = divisible by 3 and C = divisible by 5, then

n(A) = 50, n(B) = 33, n(C) = 20

n(A∩B) = 16, n(B∩C) = 6, n(A∩C) = 10

n(A∩B∩C) = 3

P(A∪B∪C) = P(A)+P(B)+P(C) – P(A∩B)-P(B∩C)-P(A∩C)+P(A∩B∩C) = 74/100

∴ Required probability is ( ) ( )P A B C 1 P A B C 0.26.∩ ∩ = − ∪ ∪ =

49. The number of distinct positive integral factors of 2014 is _________________________

Answer: (8)

Exp: 2014 = 2×19×53 i.e., product of prime factors

∴ Number of distinct positive integral factors of 2014 is (2)×(2)×(2) = 8.



28

50. Consider the following relation on subsets of the set S of integers between 1 and 2014. For

two distinct subsets U and V of S we say U < V if the minimum element in the symmetric

difference of the two sets is in U.

Consider the following two statements:

S1: There is a subset of S that is larger than every other subset.

S2: There is a subset of S that is smaller than every other subset.


(A) Both S1 and S2 are true (B) S1 is true and S2 is false

(C) S2 is true and S1 is false (D) Neither S1 nor S2 is true

Answer: (A)

Exp: From given data S1 is true ,since null set is larger than every other set ,and S2 is true since

the universal set 1,2,...,2014 is smaller than every other set.

Both s1 and s2 are true.

51. A cycle on n vertices is isomorphic to its complement. The value of n is _____.

Answer: (5)

Exp: The number of edges in Cn is n where as the number of edges in Cn’ is

2cn n−

Cycle graph Cn and its complement Cn’ have different number of edges if n≠5

Consider a cycle on five vertices 5C

'

5 5C and C areisomorphic

n 5∴ =

52. The number of distinct minimum spanning trees for the weighted graph below is

2

2

22

2 1 1

11

2

2

2

1

1v

2v

5v

4v

5v

=5

G C

1v

5v

4v

2v

3v

( ) '

5 5com plem ent of C C=5C



29

Answer: (6)

Exp: Consider the connected weighted graph (Application of Kruskal’s Algorithm)

Sort the edges by increasing edges costs (weights)

( )

1 4 2 3 4 6 5 6 8 9

3

1 2 2 4 4 3 4 5

[ v ,v , v ,v , v ,v , v ,v , v ,v Cost 1

[ v ,v , v ,v , v ,v , v ,v

−

1 5, v ,v

6 7v , v ( )7 8 7 9

2

, v ,v , v ,v cos t 2 ]−

Selection of edges of cost-1, will not form a cycle, so

Selection of 4 5v ,v and 1 5v ,v forms a cycle, so we will not consider the edges. The edge

6 7v , v can be choosen because of connectedness.

Selection of 1 2 7 8v ,v and v ,v forms one minimum spanning tree.




3 4 7 8

3 4 7 9

Selection of v , v and v ,vforms two min imum spanning trees

Selection of v , v and v ,v

∴ There are 6 distinct minimum spanning trees.

1v

5v

4v

2v

3v

6v

1 1

1 1 1

8v

7v

2

1v

5v

4v

2v

3v

6v

12

1

22

1 1

2

2

2 1

2

8v

7v2

9v

9v



30

53 Which one of the following Boolean expressions is NOT a tautology?

( ) ( ) ( )( ) ( )A a b b c a c→ ∧ → → →

( ) ( ) ( )( )B a c ~ b a c↔ → → ∧

( ) ( ) ( )C a b c c a∧ ∧ → ∧

( ) ( )D a b a→ →

Answer: (B)

Exp: (D) ( ) ( )( ) ( )( ) ( )a b a a b a a b a T tauto log y→ → ⇒ ¬ ∨ → ⇒ ¬ ∨ ¬ ∨ ⇔

(C) ( ) ( ) ( ) ( )a b c c a a b c c a∧ ∧ → ∨ ⇔ ¬ ∧ ∧ ∨ ∨

( ) ( )( ) ( )

a b c c a

a a P where P is disjunction of literals

T P T

⇔ ¬ ∨ ¬ ∨ ¬ ∨ ∨

⇔ ¬ ∨ ∨

⇔ ∨ ⇒

(a)

a b

b cby hypothetical syl logism

a c

→→

∴ →

( ) ( )( ) ( )a b b c a c→ ∧ → → → is a tautology

Answer is B which is not tautology.

54 SQL allows duplicate tuples in relations, and correspondingly defines the multiplicity of

tuples in the result of joins. Which one of the following queries always gives the same answer

as the nested query shown below:

Select * from R where a in (select S. a from S)

(A) Select R. * from R, S where R. a=S. a

(B) Select distinct R. * from R,S where R. a=S. a

(C) Select R. * from R, (select distinct a from S) as S1 where R. a=S1.a

(D) Select R. * from R, S where R.a = S. a and is unique R

Answer: (C)

Exp: Consider the following instances of R & S

a b c

1 2 3

1 2 3

3 4 5

3 4 5

a d e



31

1 2 3

2 3 4

3 4 6

3 4 6

O/P of given nested query is

a b c

1 2 3

1 2 3

3 4 5

3 4 5

(A) O/P:- multiplicity of tuples is disturbed

a b c

1 2 3

1 2 3

3 4 5

3 4 5

3 4 5

3 4 5

(B) O/P:-

a b c

1 2 3

3 4 5

(C) O/P:-

a b c Multiplicity of tuples is maintained

1 2 3

1 2 3

3 4 5

3 4 5

Multiplicity of duplicate tuples will be distributed when there is a match between R.a and

S.a and for that match S.a’s value is repeated.

55 Consider a main memory system that consists of 8 memory modules attached to the system

bus, which is one word wide. When a write request is made, the bus is occupied for 100

nanoseconds (ns) by the data, address, and control signals. During the same 100 ns, and for

500 ns thereafter, the addressed memory module executes one cycle accepting and storing the

data. The (internal) operation of different memory modules may overlap in time, but only one

request can be on the bus at any time. The maximum number of stores (of one word each)

that can be initiated in 1 millisecond is ____________



32

Answer: (10000)

Exp: Each write request, the bus is occupied for 100 n.s

Storing of data requires 100 n.s.

6

6

In 100 n.s 1 store

100n.s 1 store

10

101 m.s stores

100

10000 stores

−

=

=

=



1


1. While trying to collect an envelope from under the table, Mr. X fell down and

I II III

was losing consciousness.

IV

Which one of the above underlined parts of the sentence is NOT appropriate?

(A) I (B) II (C) III (D) IV

Answer: (D)

2. If she _______________ how to calibrate the instrument, she _______________ done the

experiment.

(A) knows, will have (B) knew, had

(C) had known, could have (D) should have known, would have

Answer: (C)

3. Choose the word that is opposite in meaning to the word “coherent”.

(A) sticky (B) well-connected (C) rambling (D) friendly

Answer: (C)

4. Which number does not belong in the series below?

2, 5, 10, 17, 26, 37, 50, 64

(A) 17 (B) 37 (C) 64 (D) 26

Answer: (C)

5. The table below has question-wise data on the performance of students in an examination.

The marks for each question are also listed. There is no negative or partial marking in the

examination.

Q.No Marks Answered

Correctly

Answered

Wrongly

Not

Attempted

1 2 21 17 6

2 3 15 27 2

3 2 23 18 3

What is the average of the marks obtained by the class in the examination?

(A) 1.34 (B) 1.74 (C) 3.02 (D) 3.91



2

Answer: (C)

Exp: Total question

44×2=88

44×3=132

144 = 88

132 308

Total marks obtained= (21×2) + (15×3) + (23×2) =133

Total Number of students=44

Average133

3.0244

= =


6. A dance programme is scheduled for 10.00 a.m. Some students are participating in the

programme and they need to come an hour earlier than the start of the event. These students

should be accompanied by a parent. Other students and parents should come in time for the

programme. The instruction you think that is appropriate for this is

(A) Students should come at 9.00 a.m. and parents should come at 10.00 a.m.

(B) Participating students should come at 9.00 a.m. accompanied by a parent, and other

parents and students should come by 10.00 a.m.

(C) Students who are not participating should come by 10.00 a.m. and they should not bring

their parents. Participating students should come at 9.00 a.m.

(D) Participating students should come before 9.00 a.m. Parents who accompany them should

come at 9.00 a.m. All others should come at 10.00 a.m.

Answer: (B)

7. By the beginning of the 20th century, several hypotheses were being proposed, suggesting a

paradigm shift in our understanding of the universe. However, the clinching evidence was

provided by experimental measurements of the position of a star which was directly behind

our sun.

Which of the following inference(s) may be drawn from the above passage?

(i) Our understanding of the universe changes based on the positions of stars

(ii) Paradigm shifts usually occur at the beginning of centuries

(iii) Stars are important objects in the universe

(iv) Experimental evidence was important in confirming this paradigm shift

(A) (i), (ii) and (iv) (B) (iii) only (C) (i) and (iv) (D) (iv) only

Answer: (D)



3

8. The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For

international comparison, the GDP is compared in US Dollars (USD) after conversion based

on the market exchange rate. During the period 2012-2013 the exchange rate for the USD

increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012-

2013

(A) increased by 5 % (B) decreased by 13%

(C) decreased by 20% (D) decreased by 11%

Answer: (D)

Exp: Per 100 Rs final value 107 Rs

100

Per Dollars50

⇒ final value 107

60

for 100 dollars____?

100 50 107

89.16100 60

×= × =

Decreased by 11%.

9. he ratio of male to female students in a college for five years is plotted in the following line

graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male

students in 2012 to male students in 2011?

(A) 1:1 (B) 2:1 (C) 1.5:1 (D) 2.5:1

Answer: (C)

Exp: Take number of female students in 2011=100

∴ Number of male in 2011=100

No. of female in 2012=100

No. of male in 2012=150

150

Ratio100

= = 1.5: 1

10. Consider the equation: (7526)8 - (Y)8 = (4364)8 , where (X) N stands for X to the base N. Find

Y.

(A) 1634 (B) 1737 (C) 3142 (D) 3162

Answer: (C)

3.5

3

2.5

2

1.5

1

0.5

02008 2009 2010 2011 2012

Ra

tio

of

m

ale

to

fe

m

ale

stu

de

nts



4


1. Consider the following statements:

P: Good mobile phones are not cheap

Q: Cheap mobile phones are not good

L: P implies Q

M: Q implies P

N: P is equivalent to Q

Which one of the following about L, M, and N is CORRECT?

(A) Only L is TRUE. (B) Only M is TRUE.

(C) Only N is TRUE. (D) L, M and N are TRUE.

Answer: (D)

Exp:

( ) [ ]( )

g : mobile is good c : mobile is cheap

P : Good mobile phones are not cheap g c g c a b a b

Q : Cheap mobile phones are not good c g c g

Both P and Q are equivalent which means P and Q imply each other

≅ → ¬ ≅ ¬ ∨ ¬ → ≡ ¬ ∨

≅ → ¬ ≅ ¬ ∨ ¬

∴

∵

2. Let X and Y be finite sets and f : X Y→ be a function. Which one of the following

statements is TRUE?

(A) For any subsets A and B of X, ( ) ( ) ( )f A B f A f B∪ = +

(B) For any subsets A and B of X, ( ) ( ) ( )f A B f A f B∩ = ∩

(C) For any subsets A and B of X, ( ) ( ) ( ) f A B min f A , f B∩ =

(D) For any subsets S and T of Y, ( ) ( ) ( )1 1 1f S T f S f T− − −∩ = ∩

Answer: (D)

Exp: ( ) ( ) ( )f : X Y defined by f a 1,f b 1,f c 2 where→ = = =

( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )

X a,b,c Y 1,2

Let A a,c ,B b,c be subsets of X

then f A B 2 ; f A 2 ; f B 2

f A B 2 ; f A 1,2 ;f B 1,2

f A f B 1,2

f A B 1

= =

= =

∪ = = =

∩ = = =

∩ =

∩ =

∴ Options (A), (B), (C) are not true

Hence, option (D) is true



5

3. Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L G≠ and that

the size of L is at least 4. The size of L is _______.

Answer: (5)

Exp: Order of subgroup divides order of group (Lagrange’s theorem).

3, 5 and 15 can be the order of subgroup. As subgroup has atleast 4 elements and it is not

equal to the given group, order of subgroup can’t be 3 and 15. Hence it is 5.

4. Which one of the following statements is TRUE about every n × n matrix with only real

eigenvalues?

(A) If the trace of the matrix is positive and the determinant of the matrix is negative, at least

one of its eigenvalues is negative.

(B) If the trace of the matrix is positive, all its eigenvalues are positive.

(C) If the determinant of the matrix is positive, all its eigenvalues are positive.

(D) If the product of the trace and determinant of the matrix is positive, all its eigenvalues are

positive.

Answer: (A)

Exp: If the trace of the matrix is positive and the determinant of the matrix is negative then atleast

one of its eigen values is negative.

Since determinant = product of eigen values.

5. If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest

possible dimension of 1 2V V∩ is _______.

Answer: (2)

Exp: Let the basis of 6-dimensional vector space be e1, e2, e3,e4, e5, e6. In order for V1 ∩ V2 to

have smallest possible dimension V1 and V2 could be, say, e1, e2, e3,e4 and e3, e4, e5,

e6 respectively. The basis of V1 ∩ V2 would then be e3, e4. => Smallest possible

dimension = 2.

6. If 2

0xsin x

π

∫ dx = kπ, then the value of k is equal to _______.

Answer: ( 4 )

Exp:

( )

( ) ( ) ( )

( ) ( ) ( )

( )

2 2

0 0

2

0

sin x sin xxsin x dx K xsin x dx xsin x dx K

x 2

x cos x 1 sin x x cos x sin x K

cos sin 0 2 cos2 sin 2 cos sin K

0 2 0 0 K 4 K k 4

π π π

π

π π

π

=−= π⇒ + − = π

π< < π

⇒ − − − − − + = π

⇒ −π π + π − − − π π+ π − −π π + π = π

⇒ π + − − π+ − π+ = π⇒ π = π ⇒ =

∫ ∫ ∫∵



6

7. Consider the following minterm expression for F.

( )F P,Q,R,S 0, 2, 5, 7, 8, 10, 13, 15=∑

The minterms 2, 7, 8 and 13 are ‘do not care terms. The minimal sum of-products form for F

is

(A) QS QS+

(B) QS QS+

(C) Q R S Q R S Q R S QRS+ + +

(B) PQS PQS PQS PQS+ + +

Answer: (B)

Exp: The K-map for the function F is as follows:-

( )1 2

1 2

P QS and P QS

F P,Q,R,S P P

QS QS

= =

∴ = +

= +

8. Consider the following combinational function block involving four Boolean variables x, y, a,

b where x, a, b are inputs and y is the output.

f (x, y, a, b)

if (x is 1) y = a;

else y = b;

Which one of the following digital logic blocks is the most suitable for implementing this

function?

(A) Full adder (B) Priority encoder (C) Multiplexor (D) Flip-flop

Answer: (C)

Exp: y xb xa= +

‘x’ is working as selection line, where the two input lines are ‘a’ and

‘b’, so the function ( )F x, y,a,b can be implemented using (2× 1)

multiplexer as follows:

9. Consider the following processors (ns stands for nanoseconds).

Assume that the pipeline registers have zero latency.

P1: Four-stage pipeline with stage latencies 1 ns, 2 ns, 2 ns, 1 ns.

P2: Four-stage pipeline with stage latencies 1 ns, 1.5 ns, 1.5 ns, 1.5 ns.

P3: Five-stage pipeline with stage latencies 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns.

P4: Five-stage pipeline with stage latencies 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns.

Which processor has the highest peak clock frequency?

(A) P1 (B) P2 (C) P3 (D) P4

Answer: (C)

PQ RS RS RS RS

PQ 1

PQ 1

PQ 1

PQ 1

φφ

φφ

RS

2P

1P

1I

0I

y

x

2 1

MUX

×a

b



7

Exp: Clock period (CP) = max stage delay + overhead

So ( )( )( )( )

P1

P2

P3

P4

CP Max 1,2,2,1 2ns

CP Max 1, 1.5, 1.5, 1.5 1.5ns

CP Max 0.5, 1,1,0.6,1 1ns

CP Max 0.5,0.5,1,1,1.1 1.1ns

= =

= =

= =

= =

As frequency 1

,C.P

α so least clock period will give the highest peak clock frequency.

p3

1So, f 1GHz

1ns= =

10. Let A be a square matrix size n n.× Consider the following pseudocode. What is the

expected output?

C = 100;

for i = 1 to n do

for j = 1 to n do

Temp = A[ i ] [ j ] + C ;

A [ i ] [ j ] = A [ j ] [ i ] ;

A [ j ] [ i ] = Temp – C ;

for i = 1 to n do

for j = 1 to n do

output (A[ i ] [ j ]);

(A) The matrix A itself

(B) Transpose of the matrix A

(C) Adding 100 to the upper diagonal elements and subtracting 100 from lower diagonal

elements of A

(D) None of these

Answer: (A)

Exp: In the computation of given pseudo code for each row and column of Matrix A, each upper

triangular element will be interchanged by its mirror image in the lower triangular and after

that the same lower triangular element will be again re-interchanged by its mirror image in

the upper triangular, resulting the final computed Matrix A same as input Matrix A.

11. The minimum number of arithmetic operations required to evaluate the polynomial

( ) 5 3P X X 4X 6x 5= + + + for a given value of X, using only one temporary variable is

_____.

Answer: (7)



8

Exp: 5 3P(x) x 4x 6x 5can be rewritten as follows= + + +

( ) ( )3 2P x x x 4 6x 5= + + +

Now using only one temporary variable t and any number of data transfer as well as memory

related operation the polynomial can be evaluated as follows

1. t x * x= [Evaluate 2x and store in memory]

2. t t 4= + [Evaluate ( )2x 4+ and store in memory]

3. 2t x= [Retinue 2x from memory]

4. t t *.X= [Evaluate 3x and store in memory]

5. ( )2t t * x 4= + [Evaluate ( )3 2x x 4+ and store in memory]

6. t 6 * x= [Evaluate 6x and store in memory]

7. t t 5= + [Evaluate ( )6x 5+ and store in memory]

8. ( )3 2t t x x 4= + + [Retrieve ( )2 2x x 4+ from memory and evaluate ( ) 3 2x x 4 6x 5+ + +

In the above 8 steps of evaluation, the total number of arithmetic operations required and 7 [4

Multiplications, 3 Additions]

So answer is 7 arithmetic operations.

12. Consider the following rooted tree with the vertex labelled P as the root

The order in which the nodes are visited during an in-order traversal of the tree is

(A) SQPTRWUV (B) SQPTUWRV

(C) SQPTWUVR (D) SQPTRUWV

Answer: (A)

Exp: The In order Traversal of Ternary Tree is done as follows:

Left Root Middle Right→ → →

So the nodes are visited in SQPTRWUV order.

P

QR

S T U V

W



9

13. Suppose depth first search is executed on the graph below starting at some unknown vertex.

Assume that a recursive call to visit a vertex is made only after first checking that the vertex

has not been visited earlier. Then the maximum possible recursion depth (including the initial

call) is _________.

Answer: 19

Exp:

Suppose, we start DFS at vertex numbered as 1 and continue calling recursive function for

DFS on subsequent nodes numbered in ascending order.

The recursive calling sequence is shown as marked line in the above diagram which shows

maximum possible recursion depth including the initial call is 19.

14. You have an array of n elements. Suppose you implement quick sort by always choosing the

central element of the array as the pivot. Then the tightest upper bound for the worst case

performance is

( ) ( )2A 0 n ( ) ( )B 0 nlog n ( ) ( )C nlog nθ ( ) ( )2

D 0 n

Answer: (A)

Exp: The Worst case time complexity of quick sort is O (n2). This will happen when the elements

of the input array are already in order (ascending or descending), irrespective of position of

pivot element in array.

15. The length of the shortest string NOT in the language ( )over a,bΣ = of the following

regular expression is _________. a*b* (ba)* a*

Answer: (3)

Exp: R.E= ( )a * b* ba *a *

Length 0 is present as it accepts ∈ all length 1 strings are present ( )a,b also aa,ab,ba,bb are

present, But 'bab ' is not present. So it is 3

1 2

46

8 10

3

5

97

17 18

1416

12

19

15

1311



10

16. Let Σ be a finite non-empty alphabet and let *2Σ be the power set of *Σ . Which one of the

following is TRUE?

(A) Both 2 *Σ and *Σ are countable

(B) 2 *Σ is countable *Σ is uncountable

(C) 2 *Σ is uncountable and *Σ is countable

(D) Both 2 *Σ and *Σ are uncountable

Answer: (C)

Exp: *2ε is the power set of *ε

*ε is countabily infinite.

The power set of countabily infinite set is uncountable.

So *2ε is uncountable, and *ε is countable.

17. One of the purposes of using intermediate code in compilers is to

(A) make parsing and semantic analysis simpler.

(B) improve error recovery and error reporting

(C) increase the chances of reusing the machine-independent code optimizer in other

compliers.

(D) improve the register allocation.

Answer: (C)

Exp: Intermediate code is machine independent code which makes it easy to retarget the compiler

to generate code for newer and different processors.

18. Which of the following statements are CORRECT?

1) Static allocation of all data areas by a compiler makes it impossible to implement

recursion.

2) Automatic garbage collection is essential to implement recursion.

3) Dynamic allocation of activation records is essential to implement recursion.

4) Both heap and stack are essential to implement recursion.

(A) 1 and 2 only (B) 2 and 3 only (C) 3 and 4 only (D) 1 and 3 only

Answer: (D)

Exp: To implement recursion, activation record should be implemented by providing dynamic

memory allocation. This dynamic allocation is done from runtime stack. Heap is essential to

allocate memory for data structures at run-time, not for recursion.

So statement 1 and 3 are correction.

19. In the context of modular software design, which one of the following combinations is

desirable?

(A) High cohesion and high coupling (B) High cohesion and low coupling

(C) Low cohesion and high coupling (D) Low cohesion and low coupling

Answer: (B)



11

Exp: Cohesion is a measure of internal strength within a module, whereas coupling is a measure of

inter dependency among the modules. So in the context of modular software design there

should be high cohesion and low coupling.

20. A system uses 3 page frames for storing process pages in main memory. It uses the Least

Recently Used (LRU) page replacement policy. Assume that all the page frames are initially

empty. What is the total number of page faults that will occur while processing the page

reference string given below?

4, 7, 6, 1, 7, 6, 1, 2, 7, 2

Answer: (6)

Exp: Page reference string is

4, 7, 6, 1, 7, 6, 1, 2, 7, 2

Implementing LRU using 3 page frames

Total page faults = 6

21. What is the optimized version of the relation algebra expression ( )( )A1 A2 F1( r )),π π σ , where

A1, A2 are sets of attributes in with 1 2

A A⊂ and F1, F2 are Boolean expressions based on

the attributes in r?

(A) ( ) ( )( )1A F1 F2 rπ σ ∧ (B) ( ) ( )( )

1A F1 F2 rπ σ ∨

(C) ( ) ( )( )2A F1 F2 rπ σ ∧ (D) ( ) ( )( )A2 F1 F2 rπ σ ∨

Answer: (A)

Exp: π is used to select a subset of attributes and pσ is used to select subset of tuples matching the

predicate P.

( )( )( )( ) ( )( )( )( )1 2 1 F 1 22

A A F A A 1 2r F F rΠ Π σ σ = Π Π σ ∧

and as 1 2A A ,⊂ so final relation will be displaying values for attributes present in set A.

( )( )( )( ) ( )( )( )1 2 1A A 1 2 A 1 2F F r F F rΠ Π σ ∧ =Π σ ∧

22. A prime attribute of a relation scheme R is an attribute that appears

(A) in all candidate keys of R. (B) in some candidate key of R.

(C) in a foreign keys of R. (D) only in the primary key of R.

Answer: (B)

Exp: A prime attribute or key attribute of a relation scheme R is an attribute that appears in any of

the candidate key of R, remaining attributes are known as non-prime or non-key tribute

23. In the following pairs of OSI protocol layer/sub-layer and its functionality, the

INCORRECT pair is

(A) Network layer and Routing

(B) Data Link Layer and Bit synchronization

(C) Transport layer and End-to-end process communication

(D) Medium Access Control sub-layer and Channel sharing

Answer: (B)

4

2

6

1

2

7



12

Exp: (a) One of the main functionality of Network Layer is Routing. So Option (a) is CORRECT.

(b) Bit Synchronization is always handled by Physical Layer of OSI model but not Data Link

Layer. So

Option (b) is INCORRECT.

(c) End – to – End Process Communication is handled by Transport Layer. So Option (c) is

CORRECT.

(d) MAC sub layer have 3 types of protocols (Random, Controlled and Channelized Access).

24. A bit-stuffing based framing protocol uses an 8-bit delimiter pattern of 01111110. If the

output bit-string after stuffing is 01111100101, then the input bit-string is

(A) 0111110100 (B) 0111110101

(C) 0111111101 (D) 0111111111

Answer: (B)

Exp: Given 8 – bit delimiter pattern of 01111110.

Output Bit string after stuffing is 01111100101

Now, Input String is 0111110101

25. Host A (on TCP/IP v4 network A) sends an IP datagram D to host B (also on TCP/IP V4

network B). Assume that no error occurred during the transmission of D. When D reaches B,

which of the following IP header field(s) may be different from that of the original datagram

D?

(i) TTL (ii) Checksum (iii) Fragment Offset

(A) (i) only (B) (i) and (ii) only

(C) (ii) and (iii) only (D) (i), (ii) and (iii)

Answer: (D)

Exp: While an IP Datagram is transferring from one host to another host, TTL, Checksum and

Fragmentation Offset will be changed.


26. An IP router implementing Classless Inter-domain routing (CIDR) receives a packet with

address 131.23.151.76. The router’s routing table has the following entries:

Prefix Output Interface Identifier

131.16.00/12 3

131.28.0.0/14 5

131.19.0.0/16 2

131.22.0.0/15 1

The identifier of the output interface on which this packet will be forwarded is _____.

StuffedBit

⇓



13

Answer: (1)

Exp: Given address 131.23.151.76.coming to the first field of given routing table

⇒ 131.16.0.0/12

131.0001 0111.151.76

131.0001 0000.0.0 (∵ given mask bits = 12)

⇒ 131.16.0.0 Matched

Coming to the 2nd

field of given Routing table

⇒ 131.28.0.0/14

131.0001 0111.151.76

131.0001 0100.0.0 (∵ given mask bits = 14)

⇒ 131.20.0.0 Not matched.

Coming to the 3rd


Error! Not a valid link. 131.19.0.0/16

131.0001 0111.151.76

131.0001 0111.0.0 (∵ given mask bits = 16)

⇒ 131.23.0.0 Not matched

Coming to the 4th


⇒ 131.22.0.0/15

131.0001 0111.151.76

131.0001 0110.0.0 (∵ given mask bits = 15)

⇒ 131.22.0.0 Matched

We are getting 1st and 4

th entries are matched so among them we have to picked up the

longest mask bit , so output interface identifier is 1.

27. Every host in an IPv4 network has a 1-second resolution real-time clock with battery backup.

Each host needs to generate up to 1000 unique identifiers per second. Assume that each host

has a globally unique IPv4 address. Design a 50-bit globally unique ID for this purpose. After

what period (in seconds) will the identifiers generated by a host wrap around?

Answer: (256)

Exp: Given that each host has a globally unique IPv4 Address and we have to design 50 – bit

unique Id. So, 50 – bit in the sense (32 + 18). So, It is clearly showing that IP Address (32 –

bit) followed by 18 bits.

1000 unique Ids => 1Sec

218

unique Ids => 218

/ 1000 = 28 = 256

28. An IP router with a Maximum Transmission Unit (MTU) of 1500 bytes has received an IP

packet of size 4404 bytes with an IP header of length 20 bytes. The values of the relevant

fields in the header of the third IP fragment generated by the router for this packet are

(A) MF bit: 0, Datagram Length: 1444; Offset: 370

(B) MF bit: 1, Datagram Length: 1424; Offset: 185

(C) MF bit: 1, Datagram Length: 1500; Offset: 370

(D) MF bit: 0, Datagram Length: 1424; Offset: 2960



14

Answer: (A)

Exp:

29. Consider the transactions T1, T2, and T3 and the schedules S1 and S2 given below.

T1 : r1 (X) ; r1 (z) ; w1 (X) ; w1 (z)

T2 : r2 (X) ; r2 (z) ; w2 (z)

T3 : r3 (X) ; r3 (X) ; w3 (Y)

S1: r1(X); r3(Y); r3(X); r2(Y); r2(Z); w3(Y); w2(Z); r1(Z); w1(X); w1(Z)

S2: r1(X); r3(Y); r2(Y); r3(X); r1(Z); r2(Z); w3(Y); w1(X); w2(Z); w1(Z)

Which one of the following statements about the schedules is TRUE?

(A) Only S1 is conflict-serializable.

(B) Only S2 is conflict-serializable.

(C) Both S1 and S2 are conflict-serializable.

(D) Neither S1 nor S2 is conflict-serializable.

Ans: (A)

Exp: Precedence graph for 1 2S &S are as follows

1S : 2S :

∴Only S1 is conflict serializable.

1T 2T

3T

Nocycle

3T 1T

2T

cycle

M

4404 bytes

Router

1500 bytes

MTU

DataLength 1480 1480 1444

HeaderLength 20 20

MF 1 1 0

+ +



15

30. Consider the relational schema given below, where eId of the relation dependentis a foreign

key referring to empId of the relation employee. Assume that every employee has at least one

associated dependent in the dependent relation.

( )employee empId, empName, empAge

dependent (depId, eId, depName, depAge)

Consider the following relational algebra query

( ) ( ) ( )empId emp Idemployee (employee empId eID emp Age depAge dependent )Π −Π = ∧ ≤

The above query evaluates to the set of empIds of employees whose age is greater than that of

(A) some dependent. (B) all dependents.

(C) some of his/her dependents. (D) all of his/her dependents

Answer: (D) A

Exp:

B

Part A of the above given relational algebra query will give the set of empIds of those

employees whose age is less than or equal to the age of some of his/her dependents.

Now when set of empIds of all employees minus set of empIds obtained from part A is done,

then we get the set of empIds of employees whose age is greater than that of all of his/her

dependents.

31. A system contains three programs and each requires three tape units for its operation. The

minimum number of tape units which the system must have such that deadlocks never arise

is _________.

Answer: (7)

Exp: Maximum Allocate Need Available

P1 -3 2 1 1

P2 -3 2 1

P3 -3 2 1

With the above given data, after allocating 2 units of tape to each process, with 1 available

unit any of the 3 process can be satisfied in such a way, that No dead lock will be there.

So answer is 7 tape units.

Q.32 An operating system uses shortest remaining time first scheduling algorithm for pre-emptive

scheduling of processes. Consider the following set of processes with their arrival times and

CPU burst times (in milliseconds):

Process Arrival Time Burst Time

P1 0 12

P2 2 4

P3 3 6

P4 8 5

The average waiting time (in milliseconds) of the processes is _________.

( ) −∏ ∏empId empId

employee ( )( ) ( )= ∧ ≤

employee dependent

empId eID empAge depAge



16

Answer: (5.5)

Exp: The Gantt chart for SRTF scheduling algorithm is as follows:

1 2 3 4 1

0 2 6 1 2 1 7 2 7

P P P P P

Average waiting time = 15 0 3 4 22

5.54 4

+ + += =

33. Consider a paging hardware with a TLB. Assume that the entire page table and all the pages

are in the physical memory. It takes 10 milliseconds to search the TLB and 80 milliseconds to

access the physical memory. If the TLB hit ratio is 0.6, the effective memory access time (in

milliseconds) is _________.

Answer: (122)

Exp: ( ) ( ) ( )ave 1 TLB M 1 TLB MT H T T 1 H T 2 T= × + + − × + ×

TLBT = time to search in TLB = 10ms

TM=time to access physical memory = 30ms

H1 = TLB hit ratio = 0.6

( ) ( )( )( )

ave

ave

ave

T 0.6 10 80 1 0.6 10 2 80

T 0.6 90ms 0.4 170 ms

T 54ms 68ms 122ms

= × + + − + ×

= × +

= + =

34. Consider the basic block given below.

a b c

c a d

d b c

e d b

a e b

= += += += −= +

The minimum number of nodes and edges present in the DAG representation of the above

basic block respectively are


Answer: (A)

Exp:

The given basic block can be rewritten as

a b c a b c

c a d c b c d

d b c d b b c d 2b c d

e d b e b

= + = += + = + += + ⇒ = + + + = + +

= − = b c d b+ + + − b c d

a e b a b b c d 2b c d

= + += + = + + + = + +

From above simplification it is visible that e is same as c and final value of a is same as d. So

the final basic block can be written as follows:



17

a b c

c a d

d 2b c d

e c

a d

= += += + +==

The DAG generated for the above basic block in as

Maximum number of modes and edges in above DAG is ( )6,6

35. Which one of the following problems is undecidable?

(A) Deciding if a given context-free grammar is ambiguous.

(B) Deciding if a given string is generated by a given context-free grammar.

(C) Deciding if the language generated by a given context-free grammar is empty.

(D) Deciding if the language generated by a given context-free grammar is finite.

Answer: (A)

Exp: There were algorithms to find the membership of CFG (using CYK algorithm) and finiteness

of CFG (using CNF graph) and emptiness. But there is no algorithm for ambiguity of CFG,

so it is undecidable.

36. Consider the following languages over the alphabet 0,1,cΣ =

n n

1

r

2

r

3

L 0 1 | n 0

L wcw | w 0,1 *

L ww | w 0,1 *

= ≥

= ∈

= ∈

Here wr is the reverse of the string w. Which of these languages are deterministic Context-

free languages?

(A) None of the languages (B) Only 1

L

(C) Only 1

L and 2

L (D) All the three languages

Answer: (C)

Exp: For the languages 1 2L and L we can have deterministic push down automata, so they are

DCFL’s, but for 3L only non-deterministic PDA possible. So the language 3L is not a

deterministic CFL.

c

d,a

d b

a

c,e

+

+

+



18

37. Suppose you want to move from 0 to 100 on the number line. In each step, you either move

right by a unit distance or you take a shortcut. A shortcut is simply a pre-specified pair of

integers i,j with

i < j. Given a shortcut i, j if you are at position i on the number line, you may directly move

to j. Suppose T(k) denotes the smallest number of steps needed to move from k to 100.

suppose further that there is at most 1 shortcut involving any number, and in particular from 9

there is a shortcut to 15. Let y and z be such that T(9) = 1 + min(T(y), T(z)). Then the value

of the product yz is_______.

Answer: (150)

Exp: By definition, T(9) = Dist. From 9 to 100

As given, T(9) = 1+min (T(y), T()z) = 1+min (Dist. from y to 100, Dist. From z to 100)

⇒1=Dist. from 9 to y/Dist. From 9 to z

⇒ There are only two such values-one is the simple one step on number line i.e. 10, and

the other is the shortcut associated with 9 i.e. 15.

⇒ Therefore, y and z are 10 and 15 (in any order)

⇒ Product yz = 150. Answer

38. Consider the decision problem 2CNFSAT defined as follows:

|φ φ is a satisfiable propositional formula in CNF with at most two literal per clause

For example, ( ) ( ) ( )1 2 1 3 2 4x v x x v x x v xφ = ∧ ∧ is a Boolean formula and it is in 2CNFSAT.

The decision problem 2CNFSAT is

(A) NP-Complete.

(B) solvable in polynomial time by reduction to directed graph reachability.

(C) solvable in constant time since any input instance is satisfiable.

(D) NP-hard, but not NP-complete.

Answer: (B)

Exp: 2 SAT is in P. This we can prove by reducing 2 SAT to directed graph reachability problem

which is known to be in P.

Procedure for reducing 2 SAT to reachability problem:

1. Let ϕ be CNF with clauses of length 2 and let P be the set of propositional

variables(literals) in ϕ

2. Build a graph G=(V,E) with V= P p|p P∪ ¬ ∈ and ( )x, y E∈ iff there is a clause in ϕ

that is equivalent to x y→ (all the clauses are converted to equivalent implications and

the graph built is called as implication graph)

3. Observe that ϕ is unsatisfiable iff there is a p P∈ such that there is both a path from p to

to p¬ and from p¬ to p in G.

This condition can be tested by running the reachability algorithm several times.

39. Suppose we have a balanced binary search tree T holding n numbers. We are given two

numbers L and H and wish to sum up all the numbers in T that lie between L and H. Suppose

there are m such numbers in T. If the tightest upper bound on the time to compute the sum is

O ( )a b c dn log n m log n+ , the value of a + 10b + 100c + 1000d is _______.



19

Answer: (110)

Exp: It takes (log n ) time to determine numbers n1 and n2 in balanced binary search tree T such

that

1. n1 is the smallest number greater than or equal to L and there is no predecessor n’1 of n1

such that n’1 is equal to n1.

2. n2 is the largest number less than or equal to H and there is no successor of n’2 of n2 such

that is equal to n2.

Since there are m elements between n1 and n2, it takes ‘m’ time to add all elements between

n1 and n2.

So time complexity is O (log n + m)

So the given expression becomes O (no log’ n + m’ log

o n)

And a+ 10b+ 100c+1000d = 0 + 10*1 + 100*1 + 1000*1 = 10 + 100 = 110

Because a = 0, b = 1, c = 1 and d =0

40. Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming

simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first

3 insertions?

(A) (97 × 97 × 97)/1003 (B) (99 × 98 × 97)/100

3

(C) (97 × 96 × 95)/1003 (D) (97 × 96 × 95)/(3! × 100

3)

Answer: (A)

Exp:A

P(First insertion in such a way that

first 3 slots are unfilled) 1

1

97C 97

100C 100= =

B

P(second insertion in such a way

that first 3 slots are

unfilled)

1

1

97C 97

100C 100= =

[∵ chaining is used to resolve

collision, so second insertion

can be done at same index as

first index ]

C

P(Third insertion in such a way

that first 3 slots are

unfilled)

1

1

97C 97

100C 100= =

[∵ Third insertion can be done at

same index as first or second

index ]

So Total prob. ( ) ( ) ( )( )

3

P A P B P C

97 97 9797 97 97

100 100 100 100

× ×

× ×= × × =

41. Consider the pseudocode given below. The function Dosomething () takes as argument a

pointer to the root of an arbitrary tree represented by the leftMostChild-rightSibling

representation. Each node of the tree is of type treeNode.



20

typedef struct treeNode* treeptr;

Struct treeNode

Treeptr leftMostchild, rightSibiling;

;

Int Dosomething (treeptr tree)

int value =0;

if (tree ! = NULL)

If (tree -> leftMostchild = = NULL)

else

value = Dosomething (tree->leftMostchild);

value = value + Dosometing (tree->rightsibiling);

return (value);

When the pointer to the root of a tree is passed as the argument to DoSomething, the value

returned by the function corresponds to the

(A) number of internal nodes in the tree.

(B) height of the tree.

(C) number of nodes without a right sibling in the tree.

(D) number of leaf nodes in the tree.

Answer: (D)

Exp: The key to solving such questions is to understand or detect where/by what condition the

value (or the counter) is getting incremented each time.

Here, that condition is if (tree→leftMostchild == Null)

⇒ Which means if there is no left most child of the tree (or the sub-tree or the current node-

as called in recursion)

⇒ Which means there is no child to that particular node (since if there is no left most child,

there is no child at all).

⇒ Which means the node under consideration is a leaf node.

⇒ The function recursively counts, and adds to value, whenever a leaf node is encountered.

⇒ The function returns the number of leaf nodes in the tree.

42. Consider the C function given below. Assume that the array listA contains n (> 0) elements,

sored in ascending order.

int ProcessArray (int * listA, int x, int n)



21

Int 1, j, k;

i = 0;

j = n – 1;

do

k = (i + j) /2;

if (x < = listA [k])

j = k – 1;

If (listA [k] < = x)

i = k+1;

while (1 < = j);

If (listA [k] = = x)

return (k) ;

else

return -1;

Which one of the following statements about the function ProcessArray is CORRECT?

(A) It will run into an infinite loop when x is not in listA.

(B) It is an implementation of binary search

(C) It will always find the maximum element in listA.

(D) It will return – 1 even when x is present in listA.

Answer: (B)

Exp: By the logic of the algorithm it is clear that it is an attempted implementation of

Binary Search. So option C is clearly eliminated. Let us now check for options A and

D.

A good way to do this is to create small dummy examples (arrays) and implement the

algorithm as it is. One may make any array of choice. Running iterations of the

algorithm would indicate that the loop exits when the x is not present. So option A is

wrong. Also, when x is present, the correct index is indeed returned. D is also wrong.

Correct answer is B. It is a correct implementation of Binary Search.

43. An instruction pipeline has five stages, namely, instruction fetch (IF), instruction decode and

register fetch (ID/RF), instruction execution (EX), memory access (MEM), and register write

back (WB) with stage latencies 1 ns, 2.2 ns, 2 ns, 1 ns, and 0.75 ns, respectively (ns stands for

nanoseconds). To gain in terms of frequency, the designers have decided to split the ID/RF

stage into three stages (ID, RF1, RF2) each of latency 2.2/3 ns. Also, the EX stage is split into

two stages (EX1, EX2) each of latency 1 ns. The new design has a total of eight pipeline

stages. A program has 20% branch instructions which execute in the EX stage and produce

the next instruction pointer at the end of the EX stage in the old design and at the end of the

EX2 stage in the new design. The IF stage stalls after fetching a branch instruction until the

next instruction pointer is computed. All instructions other than the branch instruction have

an average CPI of one in both the designs. The execution times of this program on the old and

the new design are P and Q nanoseconds, respectively. The value of P/Q is __________



22

Answer: ( 1.54 )

Exp:

No. of stages Stall cycle Stall

frequency

Clock period Avg. access

time

Old design 5 2 20% 2.2ns P

New design 8 5 20% 1 ns Q

( ) ( ) c pcompletion stall clock

P 80% 1clock 20% 1 2 T − = + + ×

( )P .8 .6 2.2ns 3.08ns= + × =

( ) ( ) c pcompletion stall clock

Q 80% 1clock 20% 1 5 T − = + + ×

( )P .8 .12 1ns 2ns= + × =

So the value of P 3.08ns

1.54Q 2ns

= =

44. The memory access time is 1 nanosecond for a read operation with a hit in cache, 5

nanoseconds for a read operation with a miss in cache, 2 nanoseconds for a write operation

with a hit in cache and 10 nanoseconds for a write operation with a miss in cache. Execution

of a sequence of instructions involves 100 instruction fetch operations, 60 memory operand

read operations and 40 memory operand write operations. The cache hit-ratio is 0.9. The

average memory access time (in nanoseconds) in executing the sequence of instructions is

__________.

Answer: (1.68)

Exp:

60memory100 instruction 40memory

Total instruction operand readfetch operation operand write op

operation

= + +

( )200 instructions operations=

Time taken for fetching 100 instructions (equivalent to read)

90*1ns 10*5ns 140ns= + =

Memory operand Read operations ( ) ( )90% 60 *1ns 10% 60 5ns= + ×

54ns 30ns 84ms= + =

Memory operands write operation time ( ) ( )90% 40 *2ns 10% 40 *10ns= +

72ns 40ns 112ns= + =

Total time taken for executing 200 instructions 140 84 112 336ns= + + =

336 ns

Average memory access time 1.68ns200

∴ = =



23

45.

The above synchronous sequential circuit built using JK flip-flops is initialized with

2 1 0Q Q Q 000.= The state sequence for this circuit for the next 3 clock cycles is

(A) 001, 010, 011 (B) 111, 110, 101

(C) 100, 110, 111 (D) 100, 011, 001

Answer: (C)

Exp:

2 1 0

P.S.

Q Q Q

2 2 1 1 0 0

FFinputs

J K J K J K

2 1 0

N.S.

Q Q Q+ + +

( ) ( ) ( ) ( ) ( ) ( )1 0 2 2 1 0Q Q Q Q Q Q

0 0 0

1 0 0

1 1 0

1 0 0 1 0 1

1 0 1 0 0 1

0 0 1 0 1 1

1 0 0

1 1 0

1 1 1

46. With respect to the numerical evaluation of the definite integral, b

2

aK x dx,= ∫ where a and b

are given, which of the following statements is/are TRUE?

(I) The value of K obtained using the trapezoidal rule is always greater than or equal to the

exact value of the definite integral.

(II) The value of K obtained using the Simpson’s rule is always equal to the exact value of

the definite integral.

(A) I only (B) II only (C) Both I and II (D) Neither I nor II

Answer: ( C )

Exp: b

2

a

x dx

let a 0, b 1

let n 4

b a 1 0h 0.25

n 4

= ==

− −⇒ = = =

∫

x 0 0.25 0.5 0.75 1

2y x= 0 0.625 0.25 0.5625 1

0y

1y 2y

3y 4y

J>K 2Q

2Q J>K

1Q

1Q

C C CJ

>K

0Q

0Q



24

I. By Trapezoidal rule

( ) ( )

( ) ( )

1

2

0 4 1 2 3

0

hx dx y y 2 y y y

2

0.250 1 2 0.0625 0.25 0.5625 0.34375

2

= + + + +

= + + + + =

∫

II. By Simpson’s 1

3 rule

( ) ( ) ( )

( ) ( ) ( )

1

2

0 4 2 1 3

0

hx dx y y 2 y 4 y y

3

0.25 10 1 2 0.25 4 0.0625 0.5625

3 3

= + + + +

= + + + + =

∫

Exact value

11 3

2

0 0

x 1x dx

3 3= =∫

47. The value of the integral given below is

2

0x cos xdx

π

∫

(A) 2− π (B) π (C) −π (D) 2π

Answer: ( A)

Exp: ( ) ( ) ( )

( ) ( )

2 2

00

2

x cos x dx x sin x 2x cos x 2 sin x

sin 2 cos 2sin 0 0 0 2

ππ

= − − + −

= π π + π π − π − + + = − π

∫

48. Let S be a sample space and two mutually exclusive events A and B be such that A B S.∪ =

If ( )P . denotes the probability of the event, the maximum value of P(A)P(B) is ______

Answer: (0.25)

Exp: Given

( ) ( )

( ) ( )

( )

( A & B are mutual

A B S

P A B P S 1

P ly exclusiA P veB 1

P B 1 P(A)

)

∪ =

⇒ ∪ = =

⇒ + =

⇒ = −

∵

Maximum value of ( ) ( )P A P B ?=

Maximum value of P (A) [1- P (A)] =?

( )

( ) ( ) 2

Let P A X

Let f x x 1 x x x

=

= − = −



25

for ( ) ( )

( )

1f x max imum f ' x 0 1 2x 0 x

2

1f " x 2; f " 0

2

⇒ = ⇒ − = ⇒ =

= − <

( )f x has max imum

1At x and maximum value

2

1 1 1 1 1 1f 1 . 0.25

2 2 2 2 2 4

∴

=

= = − = = =

49. Consider the set of all functions f : 0,1,...,2014 0,1...,2014→ such that ( )( )f f i i,= for

0 i 2014≤ ≤ . Consider the following statements.

P. For each such function it must be the case that for every i, f(i) = i,

Q. For each such function it must be the case that for some i,f(i) = i,

R. Each such function must be onto.


(A) P, Q and R are true (B) Only Q and R are true

(C) Only P and Q are true (D) Only R is true

Answer: (B)

Exp: Let us consider a function (counter example) as

( ) ( ) ( ) ( ) ( )( ) ( )

( )( )( ) ( )

f 0 1,f 1 0,f 2 3,f 3 2,....., f 2012 2013,

f 2013 2012 and f 2014 2014

Clearly f f i i for 0 i 2014

Here f i i for every i and f i i for some i

= = = = =

= =

= ≤ ≤

≠ =

Also f is onto

Hence, only Q and R are true

50. There are two elements x,y in a group (G,*) such that every element in the group can be

written as a product of some number of x’s and y’s in some order. It is known that

x * x y * y x * y *x * y y* x * y *x e= = = =

where e is the identity element. The maximum number of elements in such a group is

_________________.

Answer: (4)

Exp: x x e x is its own inverse× = ⇒



26

( ) ( ) ( )( ) ( ) ( )

[ ]( ) ( ) ( ) ( )

y y e y is its own inverse

x y x y e x y is its own inverse

y x y x e y x is its own inverse

also x x e e e can be rewritten as follows

x y y x e y y e e y y e

x y y x e shows that x y and y x

× = ⇒

× × × = ⇒ ×

× × × = ⇒ ×

× × = ×

× × × = × × × = × =

× × × = × ×

∵

Are each other’s inverse and we already know that

( ) ( )x y and y x× × are inverse of its own.

As per ( )G,* to be group any element should have

only one inverse element (unique)

This process x y y x× = × (is one element)

So the elements of such group are 4 which are x, y,e,x y×

51. If G is a forest with n vertices and k connected components, how many edges does G have?

(A) [ ]n / k (B) [ ]n / k (C) n k− (D) n k 1− +

Answer: (C)

Exp: Let 1 2 kn ,n ,.....n be the number of vertices respectively in K connected components of a

forest G, then 1 2 kn 1,n 1,....., n 1− − − be the number of edges respectively in K connected

components and 1 2 kn n ..... n n+ + + = (number of vertices in G)

Hence, number of edges in G = number of edges in K connected components

( ) ( ) ( )1 2 kn 1 n 1 ...... n 1 n k= − + − + + − = −

52. Let δ denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices

with 3,δ ≥ which one of the following is TRUE?

(A) In any planar embedding, the number of faces is at least n

22

+

(B) In any planar embedding, the number of faces is less than n

22

+

(C) There is a planar embedding in which the number of faces is less than n

22

+

(D) There is a planar embedding in which the number of faces is at most n

1δ +

Answer: (A)



27

Exp: We know that ( )v r e 2 e n r 2 ... 1+ = + ⇒ = + −

( )Where V n number of vertices ;r number of faces and

e number of edges

Given, 3 then 3n 2e

= =

=

δ ≥ ≤

( )( )

3ne

2

3nn r 2 u sin g 1

2

3n nr n 2 r 2

2 2

number of faces is atleast 2

2

⇒ ≥

⇒ + − ≥

⇒ ≥ − + ⇒ ≥ +

∴Ν +

53. The CORECT formula for the sentence, “not all rainy days are cold” is

(A) ( ) ( )( )d Rainy d Cold d∀ ∧ ∼ (B) ( ) ( )( )d Rainy d Cold d∀ →∼

(C) ( ) ( )( )d Rainy d Cold d∃ →∼ (D) ( ) ( )( )d Rainy d Cold d∃ ∧ ∼

Answer: (D)

Exp: Given statement is ( ) ( )~ d r d c d∀ →

( ) ( )

( ) ( )~ d ~ r d c d

d r d ~ c d

≡ ∀ ∨

≡ ∃ ∧

(Sin ce p q p q→ ≡ ∨∼ and let r(d) be rainy day, c(d) be cold day)

54. Consider the following relational schema:

Employee ( )empId, empName, empDept

Customer ( )custId,custName, salesRepId, rating

SalesRepId is a foreign key referring to empId of the employee relation. Assume that each

employee makes a sale to at least one customer. What does the following query return?

SELECT empName

FROM employee E

WHERE NOT EXISTS (SELECT custId

FROM customer C

WHERE C. salesRepId = E. empId

AND C. rating < > ‘GOOD’)



28

(A) Names of all the employees with at least one of their customers having a ‘GOOD’ rating.

(B) Names of all the employees with at most one of their customers having a ‘GOOD’ rating.

(C) Names of all the employees with none of their customers having a ‘GOOD’ rating.

(D) Names of all the employees with all their customers having a ‘GOOD’ rating.

Answer: (D)

Exp: The outer query will return the value (names of employees) for a tuple in relation E, only if

inner query for that tuple will return no tuple (usage of NOT EXISTS).

The inner query will run for every tuple of outer query. It selects cust-id for an employee e, if

rating of customer is NOT good. Such an employee should not be selected in the output of

outer query.

So the query will return the names of all those employees whose all customers have GOOD

rating.

55. Let ⊕ denote the Exclusive OR (XOR) operation. Let ‘1’ and ‘0’ denote the binary

constants. Consider the following Boolean expression for F over two variables P and Q.

( ) ( ) ( )( ) ( ) ( )( )F P,Q 1 P P Q P Q Q 0= ⊕ ⊕ ⊕ ⊕ ⊕ ⊕ ⊕

The equivalent expression for F is

(A) P Q+ (B) P Q+ (C) P Q⊕ (D) P Q⊕

Answer: (D)

Exp: ( ) ( ) ( )( ) ( ) ( )( )( )( ) ( )( )

( ) ( ) ( ) ( )( ) ( )

F P,Q 1 P P Q P Q Q 0

P PQ PQ PQ PQ Q

P PQ PQ P PQ PQ PQ PQ Q PQ PQ Q

PQ PQ PQ PQ Q P PQ PQ P Q

= ⊕ ⊕ ⊕ ⊕ ⊕ ⊕ ⊕

= ⊕ + ⊕ + ⊕

= + + + ⊕ + + +

= + ⊕ + = ⊕ = + = ⊕

CS-Paper Code-B GATE 2011 www.gateforum.com

© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this document may be reproduced or utilized in any form without the

written permission. Discuss GATE 2011 question paper at www.gatementor.com. 1


1. The simplified SOP (Sum of Product) form of the Boolean expression

( ) ( ) ( )P Q R . P Q R . P Q R+ + + + + + is

(A) ( )PQ R+ (B) ( )P QR+ (C) ( )PQ R+ (D) ( )PQ R+

Answer: - (B)

Exp: -

( ) ( )f P R P Q= + +

P QR= +

Alternate method

( ) ( ) ( ) ( ) ( ) ( )+ + + + + + = + + + + + +P Q R . P Q R . P Q R P Q R . P Q R . P Q R

( ) ( )

( )

P QR PQR PQR PQ R R PQR PQ PQR P Q QR

P Q R P Q R

= + + = + + = + = +

= + = +

2. Which one of the following circuits is NOT equivalent to a 2-input XNOR

(exclusive NOR) gate?

(A) (B)

(C) (D)

Answer: - (D)

Exp: - All options except option ‘D’ gives EX-NOR gates

3. The minimum number of D flip-flops needed to design a mod-258 counter is

(A) 9 (B) 8 (C) 512 (D) 258

Answer: - (A)

Exp: - n2 258 n 9≥ ⇒ =

4. A thread is usually defined as a ‘light weight process’ because an operating

system (OS) maintains smaller data structures for a thread than for a process. In

relation to this, which of the followings is TRUE?

QRP

1

0 1 1 1

00 01 11 10




(A) On per-thread basis, the OS maintains only CPU register state

(B) The OS does not maintain a separate stack for each thread

(C) On per-thread basis, the OS does not maintain virtual memory state

(D) On per thread basis, the OS maintains only scheduling and accounting

information

Answer: - (A)

5. K4 and Q3 are graphs with the following structures

Which one of the following statements is TRUE in relation to these graphs?

(A) K4 is planar while Q3 is not (B) Both K4 and Q3 are planar

(C) Q3 is planar while K4 is not (D) Neither K4 not Q3 is planar

Answer: - (B)

Exp: -

∴ Both K4 and Q3 are planar

6. If the difference between the expectation of the square of random variable

( )2E X and the square of the expectation of the random variable ( )2E X is

denoted by R then

(A) R 0= (B) R<0 (C) R 0≥ (D) R>0

Answer: - (C)

7. The lexical analysis for a modern computer language such as Java needs the

power of which one of the following machine models in a necessary and sufficient

sense?

(A) Finite state automata

(B) Deterministic pushdown automata

(C) Non-Deterministic pushdown automata

K4 Q3

4K 3Q




(D) Turing machine

Answer: - (A)

Exp: - Lexical Analysis is implemented by finite automata

8. Let the page fault service time be 10ms in a computer with average memory

access time being 20ns. If one page fault is generated for every 106 memory

accesses, what is the effective access time for the memory?

(A) 21ns (B) 30ns (C) 23ns (D) 35ns

Answer: - (B)

Exp: - P = page fault rate

EA = p × page fault service time

( )6

6 6

1 p Memory access time

1 110 10 1 20 29.9ns

10 10

+ − ×

= × × + − × ≅

9. Consider a hypothetical processor with an instruction of type LW R1, 20(R2),

which during execution reads a 32-bit word from memory and stores it in a 32-bit

register R1. The effective address of the memory location is obtained by the

addition of constant 20 and the contents of register R2. Which of the following

best reflects the addressing mode implemented by this instruction for the

operand in memory?

(A) Immediate Addressing (B) Register Addressing

(C) Register Indirect Scaled Addressing (D) Base Indexed Addressing

Answer: - (D)

Exp: - Here 20 will act as base and content of R2 will be index

10. What does the following fragment of C-program print?

( )

char c "GATE2011";char *p =c;printf "%s", p+p 3 p 1 ;

=

−

(A) GATE2011 (B) E2011 (C) 2011 (D) 011

Answer: - (C)




11. A max-heap is a heap where the value of each parent is greater than or equal to

the value of its children. Which of the following is a max-heap?

(A) (B)

(C) (D)

Answer: - (B)

Exp: - Heap is a complete binary tree

12. An algorithm to find the length of the longest monotonically increasing sequence

of numbers in an array A 0 :n 1− is given below.

Let Li denote the length of the longest monotonically increasing sequence starting

at index i in the array

Initialize Ln-1 =1

For all i such that 0 i n 2≤ ≤ −

[ ] [ ] i 1

i

1 L if A i A i 1L

1 Otherwise+

+ < +=

Finally the length of the longest monotonically increasing sequence is

( )0 1 n 1Max L ,L ,...,L − . Which of the following statements is TRUE?

(A) The algorithm uses dynamic programming paradigm

(B) The algorithm has a linear complexity and uses branch and bound paradigm

(C) The algorithm has a non-linear polynomial complexity and uses branch and bound paradigm

(D) The algorithm uses divide and conquer paradigm.

Answer: - (A)

13. Let P be a regular language and Q be a context free language such that Q P.⊆

(For example, let P be the language represented by the regular expression p*q*

and Q be ∈n np q |n N ). Then which of the following is ALWAYS regular?

(A) P Q∩ (B) −P Q (C) * P∑ − (D) * Q∑ −

10

68

4 25

1

10

68

4 25 1

10

65

4 18 2

5

82

1 104 6




Answer: - (C)

Exp: - * PΣ − is the complement of P so it is always regular,

since regular languages are closed under complementation

14. In a compiler, keywords of a language are recognized during

(A) parsing of the program (B) the code generation

(C) the lexical analysis of the program (D) dataflow analysis

Answer: - (C)

Exp: - Any identifier is also a token so it is recognized in lexical Analysis

15. A layer-4 firewall (a device that can look at all protocol headers up to the

transport layer) CANNOT

(A) block entire HTTP traffic during 9:00PM and 5:00AM

(B) block all ICMP traffic

(C) stop incoming traffic from a specific IP address but allow outgoing traffic to the same IP address

(D) block TCP traffic from a specific user on a multi-user system during 9:00PM and 5:00AM

Answer: - (A)

Exp: - Since it is a layer 4 firewall it cannot block application layer protocol like HTTP.

16. If two fair coins are flipped and at least one of the outcomes is known to be a

head, what is the probability that both outcomes are heads?

(A) 1/3 (B) 1/4 (C) 1/2 (D) 2/3

Answer: - (A)

Exp: - Sample space = HH,HT, TH

Required probability 1

3=

17. Consider different activities related to email.

m1: Send an email from a mail client to a mail server

m2: Download an email from mailbox server to a mail client

m3: Checking email in a web browser

Which is the application level protocol used in each activity?

(A) m1:HTTP m2:SMTP m3:POP (B) m1:SMTP m2:FTP m3:HTTP

(C) m1: SMTP m2: POP m3: HTTP (D) m1: POP m2: SMTP m3:IMAP

Answer: - (C)

Exp: - Sending an email will be done through user agent and message transfer agent by SMTP, downloading an email from mail box is done through POP, checking email in a web browser is done through HTTP




18. A company needs to develop a strategy for software product development for

which it has a choice of two programming languages L1 and L2. The number of lines of code (LOC) developed using L2 is estimated to be twice the LOC

developed with L1. the product will have to be maintained for five years. Various

parameters for the company are given in the table below.

Parameter Language L1 Language L2

Man years needed for development LOC / 10000 LOC / 10000

Development Cost per year Rs. 10,00,000 Rs. 7,50,000

Maintenance time 5 years 5 years

Cost of maintenance per year Rs. 1,00,000 Rs. 50,000

Total cost of the project includes cost of development and maintenance. What is the LOC for L1 for which the cost of the project using L1 is equal to the cost of

the project using L2?

(A) 4000 (B) 5000 (C) 4333 (D) 4667

Answer: - (B)

Exp: - 1

LOC L x=

2L 2x=

Total cost of project

× + × = × + ×

+ = +⇒ = −

∴ = ⇒ =

x 2x1000000 5 100000 750000 50000 5

10000 10000

100x 500000 150x 250000

50x 500000 250000

250000x x 5000

50

19. Let the time taken to switch between user and kernel modes of execution be t1 while the time taken to switch between two processes be t2. Which of the

following is TRUE?

(A) 1 2t t>

(B) 1 2t t=

(C) 1 2t t<

(D) Nothing can be said about the relation between t1 and t2

Answer: - (C)

Exp: - Process switching also involves mode changing.

20. A company needs to develop digital signal processing software for one of its

newest inventions. The software is expected to have 40000 lines of code. The company needs to determine the effort in person-months needed to develop this

software using the basic COCOMO model. The multiplicative factor for this model

is given as 2.8 for the software development on embedded systems, while the exponentiation factor is given as 1.20. What is the estimated effort in person-

months?




(A) 234.25 (B) 932.50 (C) 287.80 (D) 122.40

Answer: - (A)

Exp: - Effort person per month

( )

( )

B

1.20

. kDSI

KDSI Kilo LOC

2.8 40

2.8 83.6511

234.22 person per month

= α

=

= ×

= ×=

21. Which of the following pairs have DIFFERENT expressive power?

(A) Deterministic finite automata (DFA) and Non-deterministic finite automata (NFA)

(B) Deterministic push down automata (DPDA) and Non-deterministic push down automata (NPDA)

(C) Deterministic single-tape Turing machine and Non-deterministic single tape

Turing machine

(D) Single-tape Turing machine and multi-tape Turing machine

Answer: - (B)

Exp: - NPDA is more powerful than DPDA.

Hence answer is (B)

22. HTML (Hyper Text Markup Language) has language elements which permit certain actions other than describing the structure of the web document. Which one of the following actions is NOT supported by pure HTML (without any server

or client side scripting) pages?

(A) Embed web objects from different sites into the same page

(B) Refresh the page automatically after a specified interval

(C) Automatically redirect to another page upon download

(D) Display the client time as part of the page

Answer: - (D)

23. Which of the following is NOT desired in a good Software Requirement Specifications (SRS) document?

(A) Functional Requirements

(B) Non Functional Requirements

(C) Goals of Implementation

(D) Algorithms for Software Implementation

Answer: - (D)

24. A computer handles several interrupt sources of which the following are relevant

for this question.

Interrupt from CPU temperature sensor

Interrupt from Mouse




Interrupt from Keyboard

Interrupt from Hard Disk

(A) Interrupt from Hard Disk (B) Interrupt from Mouse

(C) Interrupt from Keyboard (D) Interrupt from CPU temp sensor

Answer: - (D)

25. Consider a relational table with a single record for each registered student with the following attributes.

1. Registration_Number: Unique registration number for each registered student

2. UID: Unique Identity number, unique at the national level for each citizen

3. BankAccount_Number: Unique account number at the bank. A student can

have multiple accounts or joint accounts. This attributes stores the primary account number

4. Name: Name of the Student

5. Hostel_Room: Room number of the hostel

Which of the following options is INCORRECT?

(A) BankAccount_Number is a candidate key

(B) Registration_Number can be a primary key

(C) UID is a candidate key if all students are from the same country

(D) If S is a superkey such that S UID is NULL then S UID ∩ ∪ is also a superkey

Answer: - (A)

Exp: - In case two students hold joint account then BankAccount_Num will not uniquely

determine other attributes.


26. Which of the given options provides the increasing order of asymptotic

complexityoffunctionsf1,f2,f3andf4?

( ) ( ) ( ) ( ) 2log nn 3 / 21 2 3 2 4f n 2 ; f n n ; f n nlog n; f n n= = = =

(A) f3, f2, f4,f1 (B) f3, f2, f1,f4 (C) f2, f3, f1,f4 (D) f2, f3, f4,f1

Answer: - (A)

Let n 1024=

( )( )( )( )

1024

1

15

2

10

3

10 100

4

3 2 4 1

f n 2

f n 2

f n 10 2

f n 1024 2

f , f , f , f is the rquired increasing order

=

=

= ×

= =

∴




27. Four matrices M1, M2, M3 and M4 are dimensions p q, q r, r s and s t× × × ×

respectively can be multiplied in several ways with different number of total

scalar multiplications. For example When multiplied as ( ) ( )( )1 2 3 4M M M M× × × the

total number of scalar multiplications is pqr+rst+prt. When multiplied as

( )( )( )1 2 3 4M M M M× × × , the total number of scalar multiplications is pqr+prs+pst.

If p=10, q=100, r=20, s=5 and t=80, then the minimum number of scalar

multiplications needed is

(A) 248000 (B) 44000 (C) 19000 (D) 25000

Answer: - (C)

Exp: - Multiply as ( )( )1 2 3 4M M M M× × ×

The total number of scalar multiplication is

qrs pqs pst

10000 5000 4000 19000

= + += + + =

28. Consider a relational table r with sufficient number of records, having attributes A1, A2,…, An and let 1 p n.≤ ≤ Two queries Q1 and Q2 are given below.

( )( )

( )( )n P

n 1 P 2

A1...A A c

A1...A c A c 1 2

Q1: r where c is a const

Q2: r where c and c are constants

=

≤ ≤

π σ

π σ

The database can be configured to do ordered indexing on Ap or hashing on Ap.

Which of the following statements is TRUE?

(A) Ordered indexing will always outperform hashing for both queries

(B) Hashing will always outperform ordered indexing for both queries

(C) Hashing will outperform ordered indexing on Q1, but not on Q2

(D) Hashing will outperform ordered indexing on Q2, but not on Q1.

Answer: - (C)

29. Consider the matrix as given below.

1 2 3

0 4 7

0 0 3

Which one of the following provides the CORRECT values of eigenvalues of the matrix?

(A) 1,4,3 (B) 3,7,3 (C) 7,3,2 (D) 1,2,3

Answer: - (A)

Exp: - Given matrix is upper triangular matrix and its diagonal elements are its eigen

values = 1, 4, 3




30. Consider an instruction pipeline with four stages (S1, S2, S3 and S4) each with

combinational circuit only. The pipeline registers are required between each stage and at the end of the last stage. Delays for the stages and for the pipeline

registers are as given in the figure.

What is the approximate speed up of the pipeline in steady state under ideal conditions when compared to the corresponding non-pipeline implementation?

(A) 4.0 (B) 2.5 (C) 1.1 (D) 3.0

Answer: - (B)

Exp: - ( )

( )5 6 11 8 30

2.511 1 12

+ + += =

+

31. Definition of a language L with alphabet a is given as following

nkL a |k 0, and n is a positive integer constant= >

What is the minimum number of states needed in a DFA to recognize L?

(A) k+1 (B) n+1 (C) 2n+1 (D) 2k+1

Answer: - (B)

Exp: - Let n = 3 and k=1

( )n 1+ states

32. An 8KB direct mapped write-back cache is organized as multiple blocks, each of

size 32-bytes. The processor generates 32-bit addresses. The cache controller

maintains the tag information for each cache block comprising of the following.

1 Valid bit

1 Modified bit

As many bits as the minimum needed to identify the memory block mapped in

the cache.

What is the total size of memory needed at the cache controller to store meta-

data (tags) for the cache?

(A) 4864 bits (B) 6144bits (C) 6656bits (D) 5376bits

Answer: - (D)

State S1Delay5ns

Pipeline RegDelay1ns

State S2Delay6ns

State S3Delay11ns


State S4Delay8ns



a a a

a

0q 1q 2q 3q




Exp: -

Required answer ( )256 19 2 5376 bits= × + =

33. An application loads 100 libraries at startup. Loading each library requires exactly

one disk access. The seek time of the disk to a random location is given as 10ms.

Rotational speed of disk is 6000rpm. If all 100 libraries are loaded from random locations on the disk, how long does it take to load all libraries? (The time to

transfer data from the disk block once the head has been positioned at the start

of the block may be neglected)

(A) 0.50s (B) 1.50s (C) 1.25s (D) 1.00s

Answer: - (B)

Exp: - 6000 rotations ________ 60 sec

1 rotation________10 ms

∴ Rotational latency = 5ms

Time for one disk access = 15 ms

Time to load all libraries 15 100 1500ms 1.5sec= × = =

34. A deterministic finite automation ( )DFA D with alphabet a,b∑ = is given below

Which of the following finite state machines is a valid minimal DFA which accepts

the same language as D?

(A) (B)

a,b a,b

a

b

a,bs

p q r

p q r

s

a

b b a,b

a

a,b

p q r

s t

a

b b a,b

a,ba

a,b

b

19 2+ 8 5

TAG

= =13

8

5

block

offset

22

2

5Byte offset 2=




(C) (D)

Answer: - (A)

Exp: - Options B and C will accept the string b

Option – D will accept the string “bba”

Both are invalid strings.

So the minimized DFA is option A

35. The following is comment written for a C function

/* This function computes the roots of a quadratic equationa.x^2+b.x+c=0. The function stores two real rootsin *root1 and *root2 and returns the status of validity of roots. It handles four different ( )( )( )( )

( ) ( )

kinds of cases.i When coefficient a is zero irrespective of discriminant

ii When discriminant is positive

iii When discrimanant is zero

iv When discrimanant is negative

Only in cases ii and iii , the stored roots are valid.Otherwise 0 is stored in the roots. the function returns 0 whenthe roots are valid and -1 otherwise.The functin also ensures root1>=root2.int get_QuadRoots float a, float b, float c, ( )float *root1, float *root2 ;* /

A software test engineer is assigned the job of doing black box testing. He comes

up with the following test cases, many of which are redundant.

Test Case

Input set Expected Output set

a b C Root1 Root2 Return

Value

T1 0.0 0.0 7.0 0.0 0.0 -1

T2 0.0 1.0 3.0 0.0 0.0 -1

T3 1.0 2.0 1.0 -1.0 -1.0 0

T4 4.0 -12.0 9.0 1.5 1.5 0

T5 1.0 -2.0 -3.0 3.0 -1.0 0

T6 1.0 1.0 4.0 0.0 0.0 -1

Which one of the following options provide the set of non-redundant tests using

equivalence class partitioning approach from input perspective for black box

testing?

(A) T1,T2,T3,T6 (B) T1,T3,T4,T5 (C) T2,T4,T5,T6 (D) T2,T3,T4,T5

Answer: - (C)

p rb a,ba,b

a,b

q

p q

s

a

b

a

a,b

b




Exp: - T1 and T2 checking same condition a = 0 hence, any one of T1 and T2 is

redundant.

T3, T4: in both case discriminant (D)=2b 4ac 0− = . Hence any one of it is

redundant.

T5 : D>0

T6 : D<0

36. Database table by name Loan_Records is given below.

Borrower Bank_Manager Loan_ Amount

Ramesh Sunderajan 10000.00

Suresh Ramgopal 5000.00

Mahesh Sunderajan 7000.00

What is the output of the following SQL query?

SELECT count(*)

FROM(

(SELECT Borrower. Bank_Manager FROM Loan_Records) AS S

NATURAL JOIN

(SELECT Bank_Manager, Loan_Amount FROM Loan_Records) AS T

);

(A) 3 (B) 9 (C) 5 (D) 6

Answer: - (C)

Exp: -

After executing the given query, the output would be

Borrower Bank_Manager Load_Amount



Suresh Ramgopal 5000.00



Borrower Bank _Manager

Ramesh Sunderajan

Suresh Ramgqpal

Mahesh Sunderjan

S

Bank _Manager Loan_ Amount

Sunderajan 10000.00

Ramgopal 5000.00

Sunderjan 7000.00

T




37. Consider two binary operators ' ' and ' '↑ ↓ with the precedence of operator ↓ being lower than that of the operator ↑ . Operator ↑ is right associative while operator ↓, is left associative. Which one of the following represents the parse tree for expression ( )7 3 4 3 2 ?↓ ↑ ↑ ↓

(A) (B)

(C) (D)

Answer: - (B)

Exp: - 7 3 4 3 2↓ ↑ ↑ ↓

( )7 3 4 3 2⇒ ↓ ↑ ↑ ↓ as ↑ is right associative

( )( )7 3 4 3 2⇒ ↓ ↑ ↑ ↓

( )( )( )7 3 4 3 2⇒ ↓ ↑ ↑ ↓ as ↓ is left associative

38. Consider the languages L1, L2 and L3 as given below

p q

p q

p q r

L1 0 1 |p,q N

L2 0 1 |p,q N and p q and

L3 0 1 0 |p,q,r N and p q r

= ∈

= ∈ =

= ∈ = =

Which of the following statements is NOT TRUE?

(A) Push Down Automata (PDA) can be used to recognize L1 and L2

(B) L1 is a regular language

(C) All the three languages are context free

(D) Turing machines can be used to recognize all the languages

7

3

4

23

7

34

2

3

7

3 4

2

3

7

3

4

2

3




Answer: - (C)

Exp: - L1: regular language

L2: context free language

L3: context sensitive language

39. On a non-pipelined sequential processor, a program segment, which is a part of the interrupt service routine, is given to transfer 500 bytes from an I/O device to memory.

Initialize the address register

Initialize the count to 500

LOOP: Load a byte from device

Store in memory at address given by address register

Increment the address register

Decrement the count

If count != 0 go to LOOP

Assume that each statement in this program is equivalent to a machine instruction which takes one clock cycle to execute if it is a non-load/store instruction. The load-store instructions take two clock cycles to execute.

The designer of the system also has an alternate approach of using the DMA controller to implement the same transfer. The DMA controller requires 20 clock cycles for initialization and other overheads. Each DMA transfer cycle takes two clock cycles to transfer one byte of data from the device to the memory.

What is the approximate speedup when the DMA controller based design is used in place of the interrupt driven program based input-output?

(A) 3.4 (B) 4.4 (C) 5.1 (D) 6.7

Answer: - (A)

Exp: - No. of clock cycles required by using load-store approach = 2 + 500 × 7 = 3502

and that of by using DMA = 20 + 500 × 2 = 1020

Required speed up 3502

3.41020

= =

40. We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree?

(A) 0 (B) 1 (C) n! (D) 2n

n

1. C

n 1+

Answer: - (D)

41. Which one of the following options is CORRECT given three positive integers x, y and z, and a predicate

( ) ( ) ( ) ( ) ( )( )P x x 1 y z x y * z y x y 1= ¬ = ∧ ∀ ∃ = ⇒ = ∨ =

(A) P(x) being true means that x is a prime number




(B) P(x) being true means that x is a number other than 1

(C) P(x) is always true irrespective of the value of x

(D) P(x) being true means that x has exactly two factors other than 1 and x

Answer: - (A)

42. Given i 1,= − what will be the evaluation of the definite integral /2

0

cos x isinxdx?

cos x isinx

π +−∫

(A) 0 (B) 2 (C) –i (D) i

Answer: - (D)

Exp: -ix

2ix2 2ix0 0

edx e dx

e

π π

−=∫ ∫

= 2ix 2

0

e

2i

π

i1e 1

2i

π = − 1cos isin 1

2i= π + π −

11 0 1

2i= − + −

2 1 i

2i i i

− −= = ×

ii

1

−= =

−

43. Consider a database table T containing two columns X and Y each of type integer. After the creation of the table, one record (X= 1, Y=l) is inserted in the table.

Let MX and MY denote the respective maximum values of X and Y among all records in the table at any point in time. Using MX and MY, new records are inserted in the table 128 times with X and Y values being MX+1, 2*MY+1 respectively. It may be noted that each time after the insertion, values of MX and MY change.

What will be the output of the following SQL query after the steps mentioned above are carried out?

SELECT Y FROM T WHERE X=7;

(A) 127 (B) 255 (C) 129 (D) 257

Answer: - (A)

Exp: -

X Y

1 1

2 3

3 7

4 15

5 31

6 63

7 127




44. Consider a finite sequence of random values 1 2 n x

X x ,x ,...x . Let= µ be the mean

and x

σ be the standard deviation of X .Let another finite sequence Y of equal

length be derived from this as i iy a* x b,= + where a and b are positive

constants. Let y

µ be the mean and y

σ be the standard deviation of this

sequence. Which one of the following statements is INCORRECT?

(A) Index position of mode of X in X is the same as the index position of mode of Y in Y.

(B) Index position of median of X in X is the same as the index position of median of Y in Y.

(C) y x

a bµ = µ +

(D) y x

a bσ = σ +

Answer: - (D)

45. A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?

(A) 1/5 (B) 4/25 (C) 1/4 (D) 2/5

Answer: - (A)

Exp: - (2,1), (3,2), (4,3), (5,4)

Required probability = 4 4 1

5 4 20 5= =

×

46. Consider the following table of arrival time and burst time for three processes P0, P1 and P2.

Process Arrival time Burst Time

P0 0 ms 9 ms

P1 1 ms 4ms

P2 2 ms 9ms

The pre-emptive shortest job first scheduling algorithm is used. Scheduling is carried out only at arrival or completion of processes. What is the average waiting time for the three processes?

(A) 5.0 ms (B) 4.33 ms (C) 6.33 ms (D) 7.33 ms

Answer: - (A)




Exp: -

4 11

Average waiting time 5 ms3

+= =

47. Consider evaluating the following expression tree on a machine with load-store

architecture in which memory can be accessed only through load and store

instructions. The variables a, b, c, d and e are initially stored in memory. The

binary operators used in this expression tree can be evaluated by the machine

only when the operands are in registers. The instructions produce result only in a

register. If no intermediate results can be stored in memory, what is the

minimum number of registers needed to evaluate this expression?

(A) 2 (B) 9 (C) 5 (D) 3

Answer: - (D)

Exp: - 1 1Load R ,a ; R M a←

2 2Load R ,b ; R M b←

1 2 1 1 2Sub R ,R ; R R R← −

2 2Load R ,c ; R M c←

3 3Load R ,d ; R M d←

2 3 2 2 3Add R , R ; R R R← +

3 3Load R ,e ; R M e←

3 2 3 3 2Sub R ,R : R R R← −

1 3 1 1 3Add R ,R ; R R R← +

Total 3 Registers are required minimum

+

− −

a b e +

c d

0P 1P 0P

2P

0 1 5 13 22





Consider the following recursive C function that takes two arguments

( )( ) ( ) ( )

unsigned int foo unsigned int n, unsigned int r

if n 0 return n%r foo n / r, r );

else return 0;

> +

48. What is the return value of the function foo when it is called as foo (513, 2)?

(A) 9 (B) 8 (C) 5 (D) 2

Answer: - (D)

Exp: -

49 What is the return value of the function foo when it is called as foo (345, 10) ?

(A) 345 (B) 12 (C) 5 (D) 3

Answer: - (B)

Exp: -

( )f 513, 2

( )f 256,2

( )f 128,2

( )f 64,2

( )f 32,2

( )f 16,2

( )f 8,2

( )f 4,2

( )f 2,2

( )f 1,2

( )f 0,2

+1

+0

+0

+0

+0

+0

+0

+0

+0

+1

+ =1 1 2

( )f 345,10

( )f 34,10

( )f 3,10

( )f 0,10

+

+

+

5

4

3+ + =5 4 3 12





Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration.

50. If all the flip-flops were reset to 0 at power on, what is the total number of distinct outputs (states) represented by PQR generated by the counter?

(A) 3 (B) 4 (C) 5 (D) 6

Answer: - (B)

Exp: -

CLOCK Inputs Outputs

=1D R ( )= +

2D P R =

3D Q R P Q R

1 0 1 0 0 1 0

2 0 1 1 0 1 1

3 1 0 0 1 0 0

4 0 0 0 0 0 0

So Total number of distinct outputs is 4

51. If at some instance prior to the occurrence of the clock edge, P. Q and R have a value 0, 1 and 0 respectively, what shall be the value of PQR after the clock edge?

(A) 000 (B) 001 (C) 010 (D) 011

PD Q

QClock

D Q

Q

D Q

Q

Q

R

Clock

Clock




Answer: - (D)

Exp: -From the Table Shown in the explanation of question 50, if first state is 010 next

State is 011



An undirected graph G(V,E) contains n ( n >2 ) nodes named 1 2 nv ,v ,....v . Two

nodes i jv , v are connected if and only if 0 i j 2.< − ≤ Each edge ( )i jv ,v is

assigned a weight i + j. A sample graph with n = 4 is shown below

52. What will be the cost of the minimum spanning tree (MST) of such a graph with n nodes?

(A) ( )2111n 5n

12− (B) 2n n 1− +

(C) 6n 11− (D) 2n 1+

Answer: - (B)

53. The length of the path from v5 to v6 in the MST of previous question with n = 10 is

(A) 11 (B) 25 (C) 31 (D) 41

Answer: - (C)

Exp: -

12 8 4 3 6 10 31+ + + + + =

7

5 6

3

4

2V1V

3V 4V

12

4

8

3

6

10

7v

5v

3v

1v 2v

4v

6v





Consider a network with five nodes, N1 to N5, as shown below

The net work uses a Distance Vector Routing protocol. Once the routes have stabilized, the distance vectors at different nodes are as following

( )( )( )( )( )

N1: 0,1,7,8,4

N2 : 1,0,6,7,3

N3: 7,6,0,2,6

N4 : 8,7,2,0,4

N5 : 4,3,6,4,0

Each distance vector is the distance of the best known path at that instance to nodes, N1 to N5, where the distance to itself is 0. Also, all links are symmetric and the cost is identical in both directions. In each round, all nodes exchange their distance vectors with their respective neighbors. Then all nodes update their distance vectors. In between two rounds, any change in cost of a link will cause the two incident nodes to change only that entry in their distance vectors

54. The cost of link N2-N3 reduces to 2 in (both directions). After the next round of updates, what will be the new distance vector at node, N3?

(A) (3. 2, 0, 2, 5) (B) (3, 2, 0, 2, 6)

(C) (7, 2, 0, 2, 5) (D) (7, 2, 0, 2, 6)

Answer: - (A)

Exp: -

55. After the update in the previous question, the link N1-N2 goes down. N2 will reflect this change immediately in its distance vector as cost, ∞ . After the NEXT ROUND of update, what will be the cost to N1 in the distance vector of N3?

(A) 3 (B) 9 (C) 10 (D) ∞

3

2

4 6

N5

N4 N3

N2

N1

3N

3

2

0

2

5

1N

2N

3N

4N

5N

1 2+

2 3+




Answer: - (C)

Exp: - N3 has neighbors N2 and N4

N2 has made entry ∞

N4 has the distance of 8 to N1

N3 has the distance of 2 to N4

So 2 + 8 = 10


56. If Log (P) = (1/2)Log (Q) = (1/3) Log (R), then which of the following options is TRUE?

(A) 2 3 2P Q R= (B) 2Q PR= (C) 2 3Q R P= (D) 2 2R P Q=

Answer: - (B)

Exp:- ( )1 1logP logQ log R k

2 3= = =

k 2k 3kP b ,Q b ,R b∴ = = =

Now, 2 4k 3k kQ b b b PR= = =

57. Choose the most appropriate word(s) from the options given below to complete the following sentence.

I contemplated________Singapore for my vacation but decided against it.

(A) To visit (B) having to visit (C) visiting (D)for a visit

Answer: - (C)

Exp: - Contemplate is a transitive verb and hence is followed by a gerund Hence the correct usage of contemplate is verb+ ing form.

58. Choose the most appropriate word from the options given below to complete the following sentence.

If you are trying to make a strong impression on your audience, you

cannot do so by being understated, tentative or_____________.

(A) Hyperbolic (B) Restrained

(C) Argumentative (D) Indifferent

Answer: - (B)

Exp: - The tone of the sentence clearly indicates a word that is similar to understated is needed for the blank. Alternatively, the word should be antonym of strong (fail to make strong impression). Therefore, the best choice is restrained which means controlled/reserved/timid.

59. Choose the word from the options given below that is most nearly opposite in meaning to the given word: Amalgamate

(A) Merge (B) Split (C) Collect (D) Separate

Answer: - (B)




Exp: - Amalgamate means combine or unite to form one organization or structure. So the best option here is split. Separate on the other hand, although a close synonym, it is too general to be the best antonym in the given question while Merge is the synonym; Collect is not related.

60. Which of the following options is the closest in the meaning to the word below:

Inexplicable

(A) Incomprehensible (B) Indelible

(C) Inextricable (D) Infallible

Answer: - (A)

Exp: - Inexplicable means not explicable; that cannot be explained, understood, or accounted for. So the best synonym here is incomprehensible.


61. P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below

A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

(A) P (B) Q (C) R (D) S

( )P 50mm

( )Q 40mm

( )R 30mm( )S 20mm

1000

800

600

400

200

0.2 0.4 0.6 0.8 1

0

To

xici

ty

(mil

lig

ram

s o

f m

icro

be

re

qu

ire

d t

o d

est

roy

ha

lf o

f th

e b

od

y

ma

ss i

n k

ilo

gra

ms)

Potency

(Probability that microbe will overcome human immunity system)




Answer: - (D)

Exp: - By observation of the table, we can say S

P Q R S

Requirement 800 600 300 200

Potency 0.4 0.5 0.4 0.8

62. The variable cost (V) of manufacturing a product varies according to the equation

V= 4q, where q is the quantity produced. The fixed cost (F) of production of same

product reduces with q according to the equation F = 100/q. How many units

should be produced to minimize the total cost (V+F)?

(A) 5 (B) 4 (C) 7 (D) 6

Answer: (A)

Exp: - Checking with all options in formula: (4q+100/q) i.e. (V+F). Option A gives the

minimum cost.

63. A transporter receives the same number of orders each day. Currently, he has

some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the

end of the 4th day he can clear all the orders. Alternatively, if he uses only 3

trucks, then all the orders are cleared at the end of the 10th day. What is the

minimum number of trucks required so that there will be no pending order at the

end of the 5th day?

(A) 4 (B) 5 (C) 6 (D) 7

Answer: - (C)

Exp: - Let each truck carry 100 units.

2800 = 4n + e n = normal

3000 = 10n + e e = excess/pending

100 8000

n ,e3 3

∴ = =

5.100 8000

5days 500x3 3

⇒ = +

8500

500x 173

⇒ = x 5⇒ >

Minimum possible = 6

64. A container originally contains 10 litres of pure spirit. From this container 1 litre

of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is

again replaced with 1 litre of water and this process is repeated one more time.

How much spirit is now left in the container?

(A) 7.58 litres (B) 7.84 litres (C) 7 litres (D) 7.29 litres




Answer: - (D)

Exp:-

3 310 1 9 729

10 1010 10 1000

− = =

729

1 7.29 litres1000

∴ × =

65. Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses

through death and parting.

Based on the above passage which topic would not be included in a unit on bereavement?

(A) how to write a letter of condolence

(B) what emotional stages are passed through in the healing process

(C) what the leading causes of death are

(D) how to give support to a grieving friend

Answer: - (C)

Exp: - The given passage clearly deals with how to deal with bereavement and grief and so after the tragedy occurs and not about precautions. Therefore, irrespective of the causes of death, a school student rarely gets into details of causes—which is beyond the scope of the context. Rest all are important in dealing with grief.



1


1. Which of the following problems are decidable?

1) Does a given program ever produce an output?

2) If L is context-free language, then, is L also context-free?

3) If L is regular language, then, is L also regular?

4) If L is recursive language, then, is L also recursive?

(A) 1,2,3,4 (B) 1,2 (C) 2,3,4 (D) 3,4

Answer:- (D)

Exp:- CFL’s are not closed under complementation. Regular and recursive languages are closed under complementation.

2. Given the language L-ab, aa, baa, which of the following strings are in L*?

1) abaabaaabaa

2) aaaabaaaa

3) baaaaabaaaab

4) baaaaabaa

(A) 1,2 and 3 (B) 2,3 and 4 (C) 1,2 and 4 (D) 1,3 and 4

Answer:-(C)

Exp:- L ab, aa, baa=

Let S1 = ab , S2 = aa and S3 =baa

abaabaaabaa can be written as S1S2S3S1S2

aaaabaaaa can be written as S1S1S3S1

baaaaabaa can be written as S3S2S1S2

3. In the IPv4 addressing format, the number of networks allowed under Class C addresses is

(A) 214 (B) 27 (C) 221 (B) 224

Answer:-(C)

Exp:- For class C address, size of network field is 24 bits. But first 3 bits are fixed as 110; hence total number of networks possible is 221

4. Which of the following transport layer protocols is used to support electronic mail?

(A) SMTP (B) IP (C) TCP (D) UDP

Answer:-(C)

Exp:- E-mail uses SMTP, application layer protocol which intern uses TCP transport layer protocol.

5. Consider a random variable X that takes values + 1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = -1 and +1 are

(A) 0 and 0.5 (B) 0 and 1



2

(C) 0.5 and 1 (D) 0.25 and 0.75

Answer:-(C)

Exp:- The cumulative distribution function

( ) ( )

( ) ( ) ( )

( ) ( ) ( ) ( )

F x P X x

F 1 P X 1 P X 1 0.5

F 1 P X 1 P X 1 P X 1 0.5 0.5 1

= ≤

− = ≤ − = = − =

+ = ≤ + = = − + = + = + =

6. Register renaming is done is pipelined processors

(A) as an alternative to register allocation at compile time

(B) for efficient access to function parameters and local variables

(C) to handle certain kinds of hazards

(D) as part of address translation

Answer:-(C)

Exp:- Register renaming is done to eliminate WAR/WAW hazards.

7. The amount of ROM needed to implement a 4 bit multiplier is

(A) 64 bits (B) 128 bits (C) 1 Kbits (D) 2 Kbits

Answer:-(D)

Exp:- For a 4 bit multiplier there are 4 4 82 2 2 256× = = combinations.

Output will contain 8 bits.

So the amount of ROM needed is 82 8 bits 2Kbits.× =

8. Let W(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. Which of the following is ALWAYS TRUE?

(A) ( ) ( )( )A n W n= Ω (B) ( ) ( )( )A n W n= Θ

(C) ( ) ( )( )A n O W n= (D) ( ) ( )( )A n o W n=

Answer:-(C)

Exp:- The average case time can be lesser than or even equal to the worst case. So A(n) would be upper bounded by W(n) and it will not be strict upper bound as it can even be same (e.g. Bubble Sort and merge sort).

( ) ( )( )A n O W n∴ =

9. Let G be a simple undirected planar graph on 10 vertices with 15edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

(A) 3 (B) 4 (C) 5 (D) 6

Answer:-(D)

Exp:- We have the relation V-E+F=2, by this we will get the total number of faces,



3

F = 7. Out of 7 faces one is an unbounded face, so total 6 bounded faces.

10. The recurrence relation capturing the optimal execution time of the Towers of Hanoi problem with n discs is

(A) ( ) ( )T n 2T n 2 2= − + (B) ( ) ( )T n 2T n 1 n= − +

(C) ( ) ( )T n 2T n / 2 1= + (D) ( ) ( )T n 2T n 1 1= − +

Answer:-(D)

Exp:- Let the three pegs be A,B and C, the goal is to move n pegs from A to C using peg B

The following sequence of steps are executed recursively

1.move n−1 discs from A to B. This leaves disc n alone on peg A --- T(n-1)

2.move disc n from A to C---------1

3.move n−1 discs from B to C so they sit on disc n----- T(n-1)

So, T(n) = 2T(n-1) +1

11. Which of the following statements are TRUE about an SQL query?

P : An SQL query can contain a HAVING clause even if it does not have a

GROUP BY clause

Q : An SQL query can contain a HAVING clause only if it has GROUP BY

clause

R : All attributes used in the GROUP BY clause must appear in the SELECT

clause

S : Not all attributes used in the GROUP BY clause need to appear in the

SELECT clause

(A) P and R (B) P and S (C) Q and R (D) Q and S

Answer:-(B)

Exp:- If we use a HAVING clause without a GROUP BY clause, the HAVING condition applies to all rows that satisfy the search condition. In other words, all rows that satisfy the search condition make up a single group. So, option P is true and Q is false.

S is also true as an example consider the following table and query.

Id Name

1 Ramesh

2 Ramesh

3 Rajesh

4 Suresh

Select count (*)

From student

Group by Name

Output will be

Count (*)

2

1



4

1

12. Given the basic ER and relational models, which of the following is INCORRECT?

(A) An attribute of an entity can have more than one value

(B) An attribute of an entity can be composite

(C) In a row of a relational table, an attribute can have more than one value

(D) In a row of a relational table, an attribute can have exactly one value or a NULL value

Answer:-(C)

Exp:- The term ‘entity’ belongs to ER model and the term ‘relational table’ belongs to relational model.

Options A and B both are true since ER model supports both multivalued and composite attributes.

As multivalued attributes are not allowed in relational databases, in a row of a relational (table), an attribute cannot have more than one value.

13. What is the complement of the language accepted by the NFA show below?

Assume a andΣ = ε is the empty string.

(A) ∅ (B) ε (C) a * (D) a, ε

Answer:- (B)

Exp:- Language accepted by NFA is a+, so complement of this language is є

14. What is the correct translation of the following statement into mathematical logic?

“Some real numbers are rational”

(A) ( ) ( )( )x real x v rational x∃ (B) ( ) ( )( )x real x rational x∀ →

(C) ( ) ( )( )x real x rational x∃ ∧ (D) ( ) ( )( )x rational x real x∃ →

Answer:- (C)

Exp:- Option A: There exists x which is either real or rational and can be both.

Option B: All real numbers are rational

Option C: There exists a real number which is rational.

Option D: There exists some number which is not rational or which is real.

15. Let A be the 2 x 2 matrix with elements a11 = a12 = a21= + 1 and a22 =-1. Then the eigen values of the matrix A19 are

(A) 1024 and -1024 (B) 1024 2 and 1024 2−

a ε

ε



5

(C) 4 2 and 4 2− (D) 512 2 and 512 2−

Answer:-(D)

Exp:- Characteristic equation of A is |A I | 0 where is the eigen value− λ = λ

2 21 1

0 2 0 21 1

− λ= ⇒ λ − = ⇒ λ = ±

− − λ

Every matrix satisfies its characteristic equation

Therefore 2 2A 2I 0 A 2I− = ⇒ =

( ) ( )

9 919 18 2

19

A A A A A 2I A 512 A

Hence eigen values of A are 512 2

= × = × = × = ×

±

16. The protocol data unit (PDU) for the application layer in the Internet stack is

(A) Segment (B) Datagram (C) Message (D) Frame

Answer:-(C)

Exp:- The PDU for Datalink layer, Network layer , Transport layer and Application layer are frame, datagram, segment and message respectively.

17. Consider the function f(x) = sin(x) in the interval [ ]x / 4,7 / 4∈ π π . The number and location

(s) of the local minima of this function are

(A) One, at / 2π (B) One, at 3 / 2π

(C) Two, at / 2π and 3 / 2π (D) Two, at / 4and3 / 2π π

Answer:-(B)

Exp:- Sin x has a maximum value of 1 at ,2

π and a minimum value of –1 at

3

2

π and at all angles

conterminal with them.

The graph of ( )f x sin x is=

7

In the int erval ,4 4

π π ∴

, it has one local minimum at

3x

2

π=

18. A process executes the code

fork ();

fork ();

fork ();

The total number of child processes created is

(A) 3 (B) 4 (C) 7 (D) 8

Answer:- (C)



6

Exp:- If fork is called n times, there will be total 2n running processes including the parent process. So, there will be 2n-1 child processes.

19. The decimal value 0.5 in IEEE single precision floating point representation has

(A) fraction bits of 000…000 and exponent value of 0

(B) fraction bits of 000…000 and exponent value of -1

(C) fraction bits of 100…000 and exponent value of 0

(D) no exact representation

Answer:-(B)

Exp:- ( ) ( ) 1

10 20.5 1.0 2−= ×

So, exponent = -1 and fraction is 000 - - - 000

20. The truth table

X Y f(X,Y)

0 0 0

0 1 0

1 0 1

1 1 1

represents the Boolean function

(A) X (B) X + Y (C) X Y⊕ (D) Y

Answer:- (A)

Exp:- ( )XY' XY X Y' Y X+ = + =

21. The worst case running time to search for an element in a balanced binary search tree with

n2n elements is

(A) ( )n log nΘ (B) ( )nn2Θ (C) ( )nΘ (D) ( )log nΘ

Answer:-(C)

Exp:- The worst case search time in a balanced BST on ‘x’ nodes is logx. So, if x = n2n, then

log(n2n) = logn + log(2n) = logn + n = θ(n)

22. Assuming P NP,≠ which of the following is TRUE?

(A) NP-complete = NP (B) NP-complete P∩ = ∅

(C) NP-hard = NP (D) P = NP-complete

Answer:-(B)

Exp:- If P!=NP, then it implies that no NP-Complete problem can be solved in polynomialtime

which implies that the set P and the set NPC are disjoint.



7

23. What will be the output of the following C program segment?

Char inChar = ‘A’ ;

switch (inChar )

case ‘A’ : printf (“Choice A\ n”);

case ‘B’ :

case ‘C’ : print f(“Choice B”);

case ‘D’ :

case ‘E’ :

default : printf (“No Choice”) ;

(A) No choice

(B) Choice A

(C) Choice A

Choice B No choice

(D) Program gives no output as it is erroneous

Answer:-(C)

Exp:- Since there is no ‘break’ statement , the program executes all the subsequent case statements after printing “choice A”

24. Which of the following is TRUE?

(A) Every relation is 3NF is also in BCNF

(B) A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R

(C) Every relation in BCNF is also in 3NF

(D) No relation can be in both BCNF and 3NF

Answer:-(C)

Exp:- Option A is false since BCNF is stricter than 3NF (it needs LHS of all FDs should be candidate key for 3NF condition)

Option B is false since the definition given here is of 2NF

Option C is true, since for a relation to be in BCNF it needs to be in 3NF, every relation in BCNF satisfies all the properties of 3NF.

Option D is false, since if a relation is in BCNF it will always be in 3NF.

25. Consider the following logical inferences.

I1 : If it rains then the cricket match will not be played.

The cricket match was played.

Inference: There was no rain.

I2 : If it rains then the cricket match will not be played.

It did not rain.

Inference: The cricket match was played.



8


(A) Both I1 and I2 are correct inferences

(B) I1 is correct but I2 is not a correct inference

(C) I1 is not correct but I2 is a correct inference

(D) Both I1 and I2 are not correct inferences

Answer:- (B)

Exp:-

( )

1

2

I : R ~ C ~RV~C

C

______

~R there was no rain

______

I : R ~ C ~Rv~C

~R ~R

______

~ RvC

______

→ ≈

→ ≈

( )1 2I is correct and I is not correct inference


26. Consider the set of strings on 0,1 in which, every substring of 3 symbols has at most two zeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings of length less than 3 are also in the language. A partially completed DFA that accepts this language is shown below.

ε

0

0

0

00

0 1

100

0 1

11

1

1

1

q 0,1

1



9

The missing arcs in the DFA are

(A) (B)

(C)

Answer:-(D)

Exp:- The complete DFA is

27. The height of a tree is defined as the number of edges on the longest path in the tree. The function shown in the pseudocode below is invoked as height (root) to compute the height of a binary tree rooted at the tree pointer root.

int height (treeptr n)

if (n== NULL) return -1;

if ( )n left NULL→ ==

00 01 10 11 q

00 1 0

01 1

10 0

11 0

00 01 10 11 q

00 0 1

01 1

10 0

11 0

00 01 10 11 q

00 1 0

01 1

10 0

11 0

00 01 10 11 q

00 1 0

01 1

10 0

11 0

ε

00

0

00

01

10 0

0 1

11

1

1

1

q 0,1

00

1 10

1

1

(D)



10

( )if n right NULL return 0;→ ==

else return BI ; // Box 1

else h1 = height (n → left);

( ) ( )if n right NULL return 1 h1 ;→ == +

else h2 height (n right);= →

return B2 ; // Box 2

The appropriate expressions for the two boxes B1 and B2 are

(A) ( )( )B1: 1 height n right+ → (B) ( )( )B1: height n right→

( )( )B2: 1 max h1,h2+ ( )( )B2: 1 max h1,h2+

(C) ( )B1: height n right→ (D) ( )( )B1: 1 height n right+ →

( )B2 : max h1,h2 ( )B2 : max h1,h2

Answer:-(A)

Exp:- int height (treeptr n)

if (n = = nu11) return – 1;

→ /* If there is no node, return -1 */

if ( )n left NULL / * If there is no left child for node 'n ' * /→ == →

( )if n right NULL return O;→ ==

/ *If no left child & no right child for→ 'n ', return */

else return (1+height ( )n right→ );

→ /* If no left child, but there is a right child, then compute height

for right sub tree. Therefore total height is 1+ height ( )n right→ */

else → / * If there exist left child node for node ‘n’ */

h1 = height ( )n left ;→

/ *→ First Find the height of left sub tree for node ‘n’ */

If ( )n right NULL→ == return ( )1 h1 ;+



11

/ *→ If there exist left child and no right child and no right child

for a node ‘n’, then total height

= height from (n to n left→ ) + left sub tree height

=1 + height ( )n left→ = 1 + h1 */

else h2 = height ( )n right→ ;

→ /* If there exist right child also, then compute height of right

sub tree for a node ‘n’ */

return ( )( )1 21 max h , h+ ;

/ *→ Total height for node ‘n’=

1 + Max (Left Subtree height, Right sub tree height)

= 1 + Max (h1, h2) */

28. Consider an instance of TCP’s Additive Increase Multiplicative decrease (AIMD) algorithm where the window size at the start of the slow start phase is 2 MSS and the threshold at the start of the first transmission is 8 MSS. Assume that a timeout occurs during the fifth transmission. Find the congestion window size at the end of the tenth transmission.

(A) 8MSS (B) 14MSS (C) 7MSS (D) 12MSS

Answer:-(C)

Exp:-

1

2

3

4

5

6

7

8

9

10

11

1

2

3

4

5

6

7

8

9

10 11 O

Timeout

Time →

congestion

window size

↑



12

Given, initial threshold = 8

Time = 1, during 1st transmission,Congestion window size = 2 (slow start phase)

Time = 2, congestion window size = 4 (double the no. of acknowledgments)

Time = 3, congestion window size = 8 (Threshold meet)

Time = 4, congestion window size = 9, after threshold (increase by one Additive increase)

Time = 5, transmits 10 MSS, but time out occurs congestion window size = 10

Hence threshold = (Congestion window size)/2 = 10 52

=

Time = 6, transmits 2


Time = 8, transmits 5 (threshold is 5)

Time = 9, transmits 6, after threshold (increase by one Additive increase)


∴ During 10th transmission, it transmits 7 segments hence at the end of the tenth transmission the size of congestion window is 7 MSS.

29. Consider a source computer (S) transmitting a file of size 106 bits to a destination computer (D) over a network of two routers (R1 and R2) and three links (L1, L2, and L3). L1 connects S to R1; L2 connects R1 to R2; and L3 connects R2 to D. Let each link be of length 100km. Assume signals travel over each line at a speed of 108 meters per second. Assume that the link bandwidth on each link is 1Mbps. Let the file be broken down into 1000 packets each of size 1000 bits. Find the total sum of transmission and propagation delays in transmitting the file from S to D?

(A) 1005ms (B) 1010ms (C) 3000ms (D) 3003ms

Answer:- (A)

Exp:-

Transmission delay for 1 packet from each of S, R1 and R2 will take 1ms

Propagation delay on each link L1, L2 and L3 for one packet is 1ms

Therefore the sum of transmission delay and propagation delay on each link for one packet is 2ms.

The first packet reaches the destination at 6thms

The second packet reaches the destination at 7thms

So inductively we can say that 1000th packet reaches the destination at 1005th ms

30. Suppose R1 ( )A, B and R2 ( )C, D are two relation schemas. Let r1 and r2 be the

corresponding relation instances. B is a foreign key that refers to C in R2. If data in r1 and r2 satisfy referential integrity constrains, which of the following is ALWAYS TRUE?

(A) ( ) ( )B 1 C 2r rΠ − Π =∅ (B) ( ) ( )C 2 B 1r rΠ − Π =∅

(C) ( ) ( )B 1 C 2r rΠ = Π (D) ( ) ( )B 1 C 2r rΠ − Π ≠∅

Answer:-(A)

S 1R

2R D

1L

2L

3L



13

Exp:- Since B is a foreign key referring C,values under B will be subset of values under C

( ( ) ( ) ( ) ( )B 1 C 2 B 1 C 2r r r rΠ ⊆ Π ⇒Π − Π =∅ )

31. Consider the virtual page reference string

1,2,3,2,4,1,3,2,4,1

on a demand paged virtual memory system running on a computer system that has main memory size of 3 page frames which are initially empty. Let LRU, FIFO and OPTIMAL denote the number of page faults under the corresponding page replacement policy. Then

(A) OPTIMAL < LRU < FIFO (B) OPTIMAL < FIFO < LRU

(C) OPTIMAL = LRU (D) OPTIMAL = FIFO

Answer:- (B)

Exp:- FIFO

1 1 1 4 4 4

2 2 2 1 1

3 3 3 2

→ (6) faults

Optimal

1 1 1 1 1

2 2 4 4

3 3 2

→ (5) faults

LRU

1 1 1 4 4 4 2 2 2

2 2 2 2 3 3 3 1

3 3 1 1 1 4 4

→ (9) faults

Optimal < FIFO < LRU

32. A file system with 300 GByte disk uses a file descriptor with 8 direct block addresses, 1 indirect block address and 1 doubly indirect block address. The size of each disk block is 128 Bytes and the size of each disk block address is 8 Bytes. The maximum possible file size in this file system is

(A) 3 KBytes (B) 35 KBytes

(C) 280 KBytes (D) dependent on the size of the disk

Answer:-(B)

Exp:- Each block size = 128 Bytes

Disk block address = 8 Bytes

∴ Each disk can contain = 128

168

= addresses

Size due to 8 direct block addresses: 8 x 128

Size due to 1 indirect block address: 16 x 128

Size due to 1 doubly indirect block address: 16 x 16 x 128

Size due to 1 doubly indirect block address: 16 x 16 x 128



14

So, maximum possible file size:

8 128 16 128 16 16 128 1024 2048 32768 35840 Bytes 35KBytes= × + × + × × = + + = =

33. Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which one will be reported by Dijkstra’s shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex v is updated only when a strictly shorter path to v is discovered.

(A) SDT (B) SBDT (C) SACDT (D) SACET

Answer:- (D)

Exp:- Let d[v] represent the shortest path distance computed from ‘S’

Initially d[S]=0, d[A] = ∞ , [ ] [ ]d B . ,d T= ∞ − − − − = ∞

And let P[v] represent the predecessor of v in the shortest path from ‘S’ to ‘v’ and let P[v]=-1 denote that currently predecessor of ‘v’ has not been computed

→ Let Q be the set of vertices for which shortest path distance has not been computed

→ Let W be the set of vertices for which shortest path distance has not been computed

→ So initially, Q = S,A,B,C,D,E,F,G,T ,W = φ

We will use the following procedure

Repeat until Q is empty

1 u = choose a vertex from Q with minimum d[u] value

2. Q Q u= −

3. update all the adjacent vertices of u

4. W = W Uu

d[S] = 0, d[A] = ∞ , d[B] = ∞ ,………, d[T] = ∞

Iteration 1

B

3

S

4

A 1

C 1 E

2

2

4

3 D

5 5

F

3

G

T

1 3

7

3 4



15

Step 1 : u = S

Step 2 : Q A,B,C,D,E,F,G,T=

Step 3: final values after adjustment

[ ] [ ] [ ] [ ] [ ] [ ] [ ]d S 0,d A 4, d B 3,d C ,d D 7,d E ,d T= = = = ∞ = = ∞ − −− = ∞

[ ] [ ] [ ] [ ] [ ] [ ]P A S, P B S,P C 1,P D S,P E 1 ,P T 1= = = − = = − − −− = −

Step 4 : W S=

Iteration 2:

[ ] [ ] [ ] [ ] [ ] [ ] [ ][ ] [ ] [ ] [ ] [ ] [ ]

Step 1: u B

Step 2 : Q A,C,D,E,F,G,T

step 3: final values after adjustment

d S 0,d A 4, d B 3,d C ,d D 7,d E ,d T

P A S, P B S,P C 1,P D S,P E 1 ,P T 1

Step 4 : W S,B

=

=

= = = = ∞ = = ∞ − −− = ∞

= = = − = = − − −− = −

=

Iteration 3:

[ ] [ ] [ ] [ ] [ ] [ ] [ ][ ] [ ] [ ] [ ] [ ] [ ]

Step 1: u A

Step 2 : Q C,D,E,F,G,T


d S 0,d A 4, d B 3,d C 5,d D 7,d E ,d T

P A S, P B S,P C A,P D S,P E 1 ,P T 1

Step 4 : W S,B,A

=

=

= = = = = = ∞ − −− = ∞

= = = = = − − −− = −

=

Iteration 4:

[ ] [ ] [ ] [ ] [ ] [ ] [ ][ ] [ ] [ ] [ ] [ ] [ ]

Step 1: u C

Step 2 : Q D,E,F,G,T


d S 0,d A 4, d B 3,d C 5,d D 7,d E 6, ,d T

P A S, P B S,P C A,P D S,P E C, ,P T 1

Step 4 : W S,B,A,C

=

=

= = = = = = − − − = ∞

= = = = = − − − = −

=

Iteration 5:



16

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

Step 1: u E

Step 2 : Q D,F,G,T


d S 0,d A 4, d B 3,d C 5,d D 7,d E 6,d F ,d G 8,d T 10

P A S, P B S,P C A,P D S,P E C,P F 1,P G E,P T E

Step 4 : W S,B,A,C,E

=

=

= = = = = = = ∞ = =

= = = = = = − = =

=

After iteration 5, we can observe that P[T]=E , P[E]=C , P[C]=A , P[A]=S,

So the shortest path from S to T is SACET

34. A list of n strings, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation is

(A) ( )O n log n (B) ( )2O n logn

(C) ( )2O n logn+ (D) ( )2O n

Answer:-(B)

Exp:- The height of the recursion tree using merge sort is logn and n2 comparisons are done at each level, where at most n pairs of strings are compared at each level and n comparisons are

required to compare any two strings, So the worst case running time is ( )2O n logn

35. Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to

(A) 15 (B) 30 (C) 90 (D) 360

Answer:- No option matching (marks to all)

Exp:- 4 vertices from 6 vertices can be chosen in in 6c4. Number of cycles of length 4 that can be formed from those selected vertices is (4-1)!/2 (left or right/ up or down does not matter), so total number of 4 length cycles are (6c4.3!)/2 = 45.

36. How many onto (or surjective) functions are there from an n-element ( )n 2≥ set to a 2-

element set?

(A) 2n (B) 2n -1 (C) 2n - 2 (D) 2(2n -2)

Answer:- (C)

Exp:- Total number of functions is 2n, out of which there will be exactly two functions where all elements map to exactly one element, so total number of onto functions is 2n-2

37. Consider the program given below, in a block-structured pseudo-language with lexical scoping and nesting of procedures permitted.

Program main;

Var . . .

Procedure A1;

Var ….



17

Call A2;

End A1

Procedure A2;

Var . . .

Procedure A21;

Var . . .

Call A1;

End A21

Call A21;

End A2

Call A1;

End main.

Consider the calling chain: Main → A1 → A2 → A21 → A1

The correct set of activation records along with their access links is given by

Answer:-(D)

Main

A1

A2

A21

A1 FRAME

POINTER ACCESS

LINKS

(A) Main

A1

A2

A21

A1 FRAME

POINTER ACCESS

LINKS

(B)

Main

A1

A2

A21

FRAME

POINTER

ACCESS

LINKS

(C) Main

A1

A2

A21

A1 FRAME

POINTER ACCESS

LINK

(D)



18

Exp:- Access link is defined as link to activation record of closest lexically enclosing block in program text, so the closest enclosing blocks respectively for A1 ,A2 and A21 are main , main and A2

38. Suppose a circular queue of capacity (n – 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operations are carried out using REAR and FRONT as array index variables, respectively. Initially, REAR = FRONT = 0. The conditions to detect queue full and queue empty are

(A) full: (REAR+1) mod n==FRONT (B) full:(REAR+1)mod n==FRONT

empty: REAR ==FRONT empty: (FRONT+1)mod n==REAR

(C) full: REAR==FRONT (D) full:(FRONT+1)mod n==REAR

empty: (REAR+1) mod n ==FRONT empty: REAR ==FRONT

Answer:- (A)

Exp:- The counter example for the condition full : REAR = FRONT is

Initially when the Queue is empty REAR=FRONT=0 by which the above full condition is satisfied which is false

The counter example for the condition full : (FRONT+1)mod n =REAR is

Initially when the Queue is empty REAR=FRONT=0 and let n=3, so after inserting one element REAR=1 and FRONT=0, at this point the condition full above is satisfied, but still there is place for one more element in Queue, so this condition is also false

The counter example for the condition empty : (REAR+1)mod n = FRONT is

Initially when the Queue is empty REAR=FRONT=0 and let n=2, so after inserting one element REAR=1 and FRONT=0, at this point the condition empty above is satisfied, but the queue of capacity n-1 is full here

The counter example for the condition empty : (FRONT+1)mod n =REAR is

Initially when the Queue is empty REAR=FRONT=0 and let n=2, so after inserting one element REAR=1 and FRONT=0, at this point the condition empty above is satisfied, but the queue of capacity n-1 is full here

39. An Internet Service Provider (ISP) has the following chunk of CIDR-based IP addresses available with it: 245.248.128.0/20. The ISP wants to give half of this chunk of addresses to Organization A, and a quarter to Organization B, while retaining the remaining with itself. Which of the following is a valid allocation of address to A and B?

(A) 245.248.136.0/21 and 245.248.128.0/22

(B) 245.248.128.0/21 and 245.248.128.0/22

(C) 245.248.132.0/22 and 245.248.132.0/21

(D) 245.248.136.0/24 and 245.248.132.0/21

Answer:- (A)

Exp:-

11110101. 11111000.1000 .− − − − − − − − − − − −

Network part host part

12 13 1

2



19

Since half of 4096 host addresses must be given to organization A, we can set 12th bit to 1 and include that bit into network part of organization A, so the valid allocation of addresses to A is 245.248.136.0/21

Now for organization B, 12th bit is set to ‘0’ but since we need only half of 2048 addresses, 13th bit can be set to ‘0’ and include that bit into network part of organization B so the valid allocation of addresses to B is 245.248.128.0/22

40. Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6?

(A) 10/21 (B) 5/12 (C) 2/3 (D) 1/6

Answer:- (B)

Exp:-

1 2 1 3 1 4 1 15 5

Required probability6 6 6 6 6 6 6 36 12

∴ = × + × + × + = =

41. Fetch_And_Add (X, i) is an atomic Read-Modify-Write instruction that reads the value of memory location X, increments it by the value i, and returns the old value of X. It is used in the pseudocode shown below to implement a busy-wait lock. L is an unsigned integer shared variable initialized to 0. The value of 0 corresponds to lock being available, while any non-zero value corresponds to the lock being not available.

AcquireLock(L)

While (Fetch_And_Add(L,1))

L = 1;

Release Lock(L)

L = 0;

This implementation

(A) fails as L can overflow

(B) fails as L can take on a non-zero value when the lock is actually available

Toss a

coin

1

2

4

6

3

5

6

5

4

6

5

4

6

3

5

1

61

61

61

61

6

2probability

6

=

3probability

6

=

4probability

6

=

1

6



20

(C) works correctly but may starve some processes

(D) works correctly without starvation

Answer:- (B)

Exp:- 1. Acquire lock (L)

2. While (Fetch_And_Add(L, 1))

3. L = 1.

4. Release Lock (L)

5. L = 0;

6.

Let P and Q be two concurrent processes in the system currently executing as follows

P executes 1,2,3 then Q executes 1 and 2 then P executes 4,5,6 then L=0 now Q executes 3

by which L will be set to 1 and thereafter no process can set

L to zero, by which all the processes could starve.

42. Consider the 3 process, P1, P2 and P3 shown in the table.

Process Arrival time Time units Required

P1 0 5

P2 1 7

P3 3 4

The completion order of the 3 processes under the policies FCFS and RR2 (round robin

scheduling with CPU quantum of 2 time units) are

(A) FCFS: P1, P2, P3 RR2: P1, P2, P3

(B) FCFS: P1, P3, P2 RR2: P1, P3, P2

(C) FCFS: P1, P2, P3 RR2: P1, P3, P2

(D) FCFS: P1, P3, P2 RR2: P1, P2, P3

Answer:-(C)

Exp:- For FCFS Execution order will be order of Arrival time so it is P1,P2,P3

Next For RR with time quantum=2,the arrangement of Ready Queue will be as follows:

RQ: P1,P2,P1,P3,P2,P1,P3,P2

This RQ itself shows the order of execution on CPU(Using Gantt Chart) and here it gives the

completion order as P1,P3,P2 in Round Robin algorithm.



21

43. What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t

care term.

(A) bd (B) bd bc+

(C) bd abcd+ (D) bd bc cd+ +

Answer:- (B)

Exp:-

X

d 'b ' c 'b '+

44. Let G be a weighted graph with edge weights greater than one and G’ be the graph constructed by squaring the weights of edges in G. Let T and T’ be the minimum spanning trees of G and G’ respectively, with total weights t and t’. Which of the following statements is TRUE?

(A) T’ = T with total weight t’ = t2 (B) T’ = T with total weight t’ < t2

(C) T’ ≠ T but total weight t’ = t2 (D) None of these

Answer:-(D)

Exp:-

Graph G is counter example for options (B) and (C) and Graph G1 is counter example for option (A)

cd

ab 00 01 11 10

00

01

11

10

1 X X 1

1

X

X

1

cd

ab 00 01 11 10

00

01

11

10

1 X 1

1

X

X

1

2

G

2 3

G1



22

45. The bisection method is applied to compute a zero of the function f(x) = x4 -x3 - x2 – 4 in the interval [1,9]. The method converges to a solution after ______ iterations.

(A) 1 (B) 3 (C) 5 (D) 7

Answer:- (B)

Exp:-

( )

( ) ( )

( ) [ ]

4 3 2

0

f x x x x 4

1 9f 1 0 and f 9 0 x 5

2

f 5 0 root lies in 1,5

= − − −

+< > ∴ = =

> ∴

( ) [ ]

( )

1

2

1 5x 3

2

f 3 0 root lies in 1,3

1 3x 2

2

f 2 0 root is 2

+= =

> ∴

+= =

= ∴

46. Which of the following graph is isomorphic to

(A) (B)

(C) (D)

Answer:-(B)

Exp:- The graph in option (A) has a 3 length cycle whereas the original graph does not have a 3 length cycle

The graph in option (C) has vertex with degree 3 whereas the original graph does not have a vertex with degree 3



23

The graph in option (D) has a 4 length cycle whereas the original graph does not have a 4 length cycle

47. Consider the following transactions with data items P and Q initialized to zero:

T1 : read (P) ;

read (Q) ;

if P = 0 then Q : = Q + 1 ;

write (Q).

T2 : read (Q) ;

read (P)

if Q = 0 then P : = P + 1 ;

write (P).

Any non-serial interleaving of T1 and T2 for concurrent execution leads to

(A) a serializable schedule

(B) a schedule that is not conflict serializable

(C) a conflict serializable schedule

(D) a schedule for which precedence graph cannot be drawn

Answer:-(B)

Exp:- Let S be a non-serial schedule, without loss of generality assume that T1 has started earlier than T2. The first instruction of T1 is read(P) and the last instruction of T2 is write(P), so the precedence graph for S has an edge from T1 to T2, now since S is a non-serial schedule the first instruction of T2(read(Q)) should be executed before last instruction of T1(write(Q)) and since read and write are conflicting operations, the precedence graph for S also contains an edge from T2 to T1, So we will have a cycle in the precedence graph which implies that any non serial schedule with T1 as the earliest transaction will not be conflict serializable.

In a similar way we can show that if T2 is the earliest transaction then also the schedule is not conflict serializable.


Consider the following relations A, B and C:

A

Id Name Age

12 Arun 60

15 Shreya 24

99 Rohit 11

B

Id Name Age

15 Shreya 24

25 Hari 40



24

98 Rohit 20

99 Rohit 11

C

Id Phone Area

10 220 02

99 2100 01

48. How many tuples does the result of the following SQL query contain?

SELECT A.Id

FROM A

WHERE A.Age > ALL(SELECT B.Age

FROM B

WHERE B.Name = ‘Arun’)

(A) 4 (B) 3 (C) 0 (D) 1

Answer:-(B)

Exp:- As the result of subquery is an empty table, ‘>ALL’ comparison is true . Therefore, all the three row id’s of A will be selected from table A.

49. How many tuples does the result of the following relational algebra expression contain? Assume that the schema of A B∪ is the same as that of A.

( ) A.Id 40 v C.Id 15A B C> <∪

(A) 7 (B) 4 (C) 5 (D) 9

Answer:-(A)

Exp:- The final table is

AUB . Id Name Age C.Id Phone Area

12 Arun 60 10 2200 02

15 Shreya 24 10 2200 02

25 Hari 40 10 2200 02

98 Rohit 20 10 2200 02

98 Rohit 20 99 2100 01

99 Rohit 11 10 2200 02

99 Rohit 11 99 2100 01


Consider the following C code segment:

int a, b, c = 0;

void prtFun(void);



25

main( )

static int a = 1; /* Line 1 */

prtFun( );

a + = 1;

prtFun( )

printf(“\n %d %d “, a, b);

void prtFun(void)

static int a=2; /* Line 2 */

int b=1;

a+=++b;

printf(“\n %d %d “, a, b);

50. What output will be generated by the given code segment if:

Line 1 is replaced by auto int a = 1;

Line 2 is replaced by register int a = 2;

(A) (B) (C) (D)

3 1

4 1

4 2

4 2

6 1

6 1

4 2

6 2

2 0

4 2

4 2

2 0

Answer:-(D)

Exp:- Static local variables: Scope is limited to function/block but life time is entire program.

Automatic local variables:

Storage allocated on function entry and automatically deleted or freed when the function is exited.

Register variables: Same as automatic variables except that the register variables will not have addresses Hence may not take the address of a register variable.

a b a 0

b 0

c 0

a 1

2

( )main 2

4

1

2

( )pr int s : 4 2 1→ ( )1

( )→pr int s : 2, 0 3

4

a

4

1

b

2

( )pr int s : 4 2 2→ ( )2



26

51. What output will be generated by the given code segment?

(A) (B) (C) (D)

3 1

4 1

4 2

4 2

6 1

6 1

4 2

6 2

2 0

3 1

5 2

5 2

Answer:- (C)

Exp:-



A computer has a 256 KByte, 4-way set associative, write back data cache with block size of 32 Bytes. The processor sends 32 bit addresses to the cache controller. Each cache tag directory entry contains, in addition to address tag, 2 valid bits, 1 modified bit and 1 replacement bit.

52. The number of bits in the tag field of an address is

(A) 11 (B) 14 (C) 16 (D) 27

Answer:- (C)

Exp:- Number of blocks = 18

13

5

256 KB 22 blocks

32Bytes 2= =

As it is 4–way set associative, number of sets = 13

11

2

22

2=

32 bits

TAG SET

offset Byte offset

5 11 16

a 0

b 0

c 0

a 1

2

( )main 2

4

a

1 2

( )pr int s : 4 2 1→ ( )1

pr int s : 2,0

( )2

b

4 6

a

1 2

( )static keeps old value

b ( )pr int : 6,2 2→ 4 2

6 2

2 0



27

53. The size of the cache tag directory is

(A) 160 Kbits (B) 136 Kbits (C) 40 Kbits (D) 32 Kbits

Answer:-(A)

Exp:- TAG controller maintains 16 + 4 = 20 bits for every block

Hence, size of cache tag directory = 1320 2× bits =160 K bits


For the grammar below, a partial LL(1) parsing table is also presented along with the grammar. Entries that need to be filled are indicated as E1, E2, and E3. ε is the empty string, $ indicates end of input, and | separates alternate right hand sides of productions.

S a AbB bAa B→ ε

A S→

B S→

a b $

S E1 E2 S → ε

A A S→ A S→ error

B B S→ B S→ E3

54. The First and Follow sets for the non-terminals A and B are

(A) FIRST(A) = a, b, ε = FIRST (B)

FOLLOW(A) = a, b

FOLLOW(B) = a, b, $

(B) FIRST(A) = a, b, $

FIRST(B) = a, b, ε

FOLLOW(A) = a, b

FOLLOW(B) =$

(C) FIRST(A) = a, b, ε = FIRST(B)

FIRST(A) = a, b

FOLLOW(B) = ∅

(D) FIRST(A) = a, b, = FIRST(B)

FIRST(A) = a, b

FOLLOW(B) =a, b

Answer:- (A)

Exp:- ( ) ( ) ( ) ( ) ( )First A First S First aAbB First bAaB First= = ∪ ∪ ∈

( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

a b ,a,b

First B First S ,a,b

Follow A First bB First aB a,b

Follow B Follow S $ Follow A $, a,b

= ∪ ∪ ∈ = ∈

= = ∈

= ∪ =

= = ∪ =



28

55. The appropriate entries for E1, E2, and E3 are

(A) E1: S aAbB, A S→ → (B) E1: S aAbB, S→ → ε

E2: S bAaB, B S→ →

E2: S bAaB, S→ → ε

E3: B S→ E3: S → ε

(C) E1: S aAbB, S→ → ε (D) E1: A S, S→ → ε

E2: S bAaB, S→ → ε E2: B S, S→ → ε

E3: B S→ E3: B S→

Answer:- (C)

Exp:-

( ) ( ) First S ,a,b , Follow S $,a,b

a b $

S S aAbB S bAaB S

S S

= ∈ =

→ → →∈

→∈ →∈

B S→ to be placed in LL(1) Parsing table as follows:-

( ) ( ) First S ,a,b , Follow B $,a,b

a b $

B B S B S B S

= ∈ =

→ → →


56. The cost function for a product in a firm is given by 25q , where q is the amount of

production. The firm can sell the product at a market price of Rs.50 per unit. The number of units to be produced by the firm such that the profit is maximized is

(A) 5 (B) 10 (C) 15 (D) 25

Answer:- (A)

Exp:-

2

2

2

P 50q 5q

dp d p50 10q; 0

dq dq

p is max imum at 50 10q 0 or, q 5

= −

= − <

∴ − = =

Else check with options

57. Choose the most appropriate alternative from the options given below to complete the following sentence:

Suresh’s dog is the one ________ was hurt in the stampede.

(A) that (B) which (C) who (D) whom

Answer:- (A)



29

58. Choose the grammatically INCORRECT sentence:

(A) They gave us the money back less the service charges of Three Hundred rupees.

(B) This country's expenditure is not less than that of Bangladesh.

(C) The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser sum.

(D) This country's expenditure on educational reforms is very less

Answer:-(D)

59. Which one of the following options is the closest in meaning to the word given below?

Mitigate

(A) Diminish (B) Divulge (C) Dedicate (D) Denote

Answer:- (A)

60. Choose the most appropriate alternative from the options given below to complete the following sentence:

Despite several __________ the mission succeeded in its attempt to resolve the conflict.

(A) attempts (B) setbacks (C) meetings (D) delegations

Answer:- (B)


61. Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.

Which one of the following is the best inference from the above advertisement?

(A) Gender-discriminatory (B) Xenophobic

(C) Not designed to make the post attractive (D) Not gender-discriminatory

Answer:- (C)

Exp:- Gender is not mentioned in the advertisement and (B) clearly eliminated

62. Given the sequence of terms, AD CG FK JP, the next term is

(A) OV (B) OW (C) PV (D) PW

Answer:- (A)

Exp:-

63. Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list

Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list

R: Doubling each entry in a list doubles the mean of the list

AD , CG , FK , JP , OV

2+ 3+ 4+ 5+

3+ 4+ 5+ 6+



30

S: Doubling each entry in a list leaves the standard deviation of the list unchanged

(A) P, Q (B) Q, R (C) P, R (D) R, S

Answer:-(C)

Exp:- P and R always hold true

Else consider a sample set 1, 2, 3, 4 and check accordingly

64. An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable Of X's shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

(A) 0.288 (B) 0.334 (C) 0.667 (D) 0.720

Answer:-(B)

x y

Exp:- Supply 60% 40%

Reliable 96% 72%

Overall 0.576 0.288

( ) 0.288P x 0.334

0.576 0.288∴ = =

+

65. A political party orders an arch for the entrance to the ground in which the annual convention is

being held. The profile of the arch follows the equation 2y 2x 0.1x= − where y is the height of

the arch in meters. The maximum possible height of the arch is

(A) 8 meters (B) 10 meters (C) 12 meters (D) 14 meters

Answer:-(B)

Exp:-

2

2

2

y 2x 0.1x

dy2 0.2x

dx

d y0 y max imises at 2 0.2x 0

dx

x 10

y 20 10 10m

= −

= −

< ∴ − =

⇒ =

∴ = − =

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