usn: 4 m c malnad college of engineering,...

III

USN: 4 M C

MALNAD COLLEGE OF ENGINEERING, HASSAN Seventh Semester B.E - (Autonomous Program)

Semester End Examinations December 2013 / January 2014

Course Title : Engineering Mathematics-III Course Code : MA 301

Duration : 3 Hours Maximum Marks : 100

Instructions to the Candidates :

i) Answer any FIVE full questions choosing atleast one from each part.

ii) Missing data, if any, may suitably be assumed.

iii) On completing your answers, compulsorily draw diagonal cross lines on the remaining blank pages.

PART – A

1. a) Find the Fourier series expansion of f(x) = 2x-x2 in (0, 2). 07

b) Find the half-range cosine series of f(x) = x; 0 < x < 2

= - x, x

< x <

07

c) Express y as a Fourier series upto first harmonics, given

x 0 3

32 3

4 3

5 2

y 1.98 1.30 1.05 1.30 -0.88 -0.25 1.98

06

2. a) Find the Fourier transform of f(x) = 1-x2, |x| 1

0, |x| > |

& hence evaluate dxx

x

xxx

2cos

sincos

0

3

07

b) Find the Fourier cosine transform of e-x2. 07

c) Obtain the Fourier sine transform of 4x for 9 < x < 1

f(x) = 4-x for 1 < x < 4

0 for x > 4

06

PART – B

3. a) Find z [ kn cos n ] & hence deduce a[e-an cos n] 07

b) Using 2)1(

)(

z

znz find z(n2) & hence show that z[(n+1)2] =

3

23

)1(

z

zz

07

c) Solve by using z-transform yn+2 – 4yn=0 given that y0 = 0, y1=2.

06

4. a) Explain Bisection method to find the real root of the equation f(x) = 0 and hence find an

approximate root of the equation sin x = x

1 that lies between x=1 & x = 1.5 (measured in

radius). Carryout four step.

07

b) Deduce an iterative formula to find cube root of N using Newton – Raphson formula & hence

evaluate 3 10 . Correct to four decimals.

07

c) Solve the non-linear equations x2-y2 = 4, x2+y2 = 16 numerically with xo = yo = 2.828 with one

step.

06

P.T.O.

MA 301

PART – C

5. a) In a table given below, the values of y are consecutive terms of a series of which 23.6 is the 6th

term. Find the first & tenth terms of the series, using appropriate inter polation formula.

x 3 4 5 6 7 8 9

y 4.8 8.4 14.5 23.6 36.2 52.8 73.9

07

b) Apply Bessel’s formula to obtain y25, given y20 = 2854, y24 = 3162, y28 =3544, y32 = 3992. 07

c) The pressure P of wind corresponding to velocity V is given by the following data. Estimate

P when V=25 using stirling’s formula

V 10 20 30 40

P 1.1 2 4.4 7.9

06

6. a) If y(1) = -3, y(30=9, y(4) = 30, y(6) = 132. find the Lagrange’s interpolation polynomial that

takes the same values as y at the given points.

07

b) Using Newton’s divided difference formula evaluate f(15), given

x 4 5 7 10 11 13

f(x) 48 100 294 900 1210 2028

07

c) Using Newton’s forward interpolation formula. Find y (0.6) & y (0.6) from the following

table.

x 0 0.2 0.4 0.6 0.8 1.0 1.2

y 0 1.12 0.49 1.12 2.02 3.20 4.67

06

PART – D

7.

a) by dividing the range into ten equal parts evaluate

0

sin dxx by Trapezoidal rule. 07

b) By dividing the range into ten equal parts evaluate

6.0

0

2

dxe x by taking seven ordinates.

07

c) Using Gaussian quadrature two points formula evaluate

1

01 x

dx

(Take c1 = c2=1, t1 = -0.57735, t2 = 0.57735)

06

8. a) Use Gauss elimination method to solve the system.

2x1 – x2 + x3 + 0x4 = 01

0x1 + 2x2 – x3 + x4 = 1

x1 + 0x2 + 2x3 – x4 = -1

x1 + x2 + 0x3 + 2x4 = 3

07

b) Use L-U decomposition method to solve the system

x + 5y + z = | 4

2x + y + 3z = | 3

3x + y + 4z = | 7

07

c) Find all eigen values and the corresponding eigen vectors of the matrix for lease eigen value.

021

612

322

A

06

V

USN: 4 M C

MALNAD COLLEGE OF ENGINEERING, HASSAN Fifth Semester B.E - (Autonomous Program)


Course Title : Graph theory & Combinatorics Course Code : IS 501






PART – A

1. a) Explain the following with suitable examples:

i) Subgraph (ii) Induced subgraph (iii) Euler circuit (iv) Euler trial.

04

b) What is graph isomorphism? Identify whether the given 2 graphs are isomorphic or not?

Justify your answer.

07

c) Seven towns a, b, c, d, e, f and g are connected by a system of highways as follows:

i) I-22 goes from a to c passing through b

ii) I-33 goes from c to d & then passes through b as it continues to f.

iii) I-44 goes from d through e to a

iv) I-55 goes from f to b passing through g &

v) I-66 goes from g to d.

a) Using vertices for towns & directed edges for segments of highways between towns, draw a

directed graph that models this situation.

b) List the paths from g to a.

c) What is the smallest number of highway segments that would have to be closed down in

order for travel from b to d.

d) Is it possible to leave town C & return there, visiting each of the towns only once?

e) Is it possible to start at some town & drive over each of these highways exactly once? Also

write the trial.

09

2. a) If G=(V, E) be a connected planar graph or multigraph and be the number of regions in the

plane determined by a planar embedding of G, one of these regions has in finite area & is

called infinite region. Then prove that V-C+r = 2.

07

b) Explain the following with suitable examples.

i) Bipartite graph (ii) Complete bipartite graph (iii) Elementary subdivision & (iv) Planar

graph

06

c) Prove that a graph is nonplanar if and only if contains a subgraph that is homeomorphic to

either K5 or K3,3.

07

P.T.O.

IS 501

PART – B

3. a) What is a chromatic polynomial & chromatic number? By using the decomposition theorem

find the chromatic polynomial & chromatic number for the given graph.

12

b) Obtain the dual of the given graph. List all the steps followed in the process of obtaining the

dual graph.

08

4. a) Construct the optimal prefix code for the letters in the sentence INCREDIBLE INDIA. &

hence deduce the code for this.

08

b) Prove that in every tree T=(V, E), |V| = |E| +1. 05

c) For the given network find the maximum possible flow between vertex A & vertex Z using

maxflow min cut theorem. List all a=z cut.

07

PART – C

5. a) State Sum Rule & the Product Rule. 05

b) How many arrangements are there for all letters in the word SOCIOLOGICAL? In how many

of these arrangements A & G are adjacent and all the vowels are adjacent.

08

c) Determine the coefficient of

i) xyz2 in (x+y+z)4 (ii) xyz2 in (2x-y-z)4 (iii) a2b3c2d5 in (a+2b-3c+2d+5)16.

07

6. a) What is an Catalan sequence? In how many ways one can arrange four 1’s & four – 1’s so

that all eight partial sums are non negative.

05

b) Find the Catalan number of b10 b9 & b8. 05

c) Determine the number of positive integer n such that 1 n 100 & n is not divisible by 2, 3

or 5.

10

PART – D

7. a) How many derangements are there for 1, 2, 3, 4, 5? 04

b) Find the Rook polynomial for the board shown below (Numbered part).

1 2

3 4

5 6

7 8

07

9 10 11

P.T.O.

IS 501

c) Find the sequence Generated by the functions:

i) (3+x)3 (ii) 321

1x

x

04

d) Find the generating functions for the following sequences.

i) 02, 12, 22, 32 _ _ _ _ (ii) 1, -2, 3, -4 _ _ _ _

05

8. a) Using generating functions, find the partitions of n=6. 08

b) For each of the words given below, find the exponential generating function for the number of

ways to arrange n 11 letters selected from the word.

i)ISOMORPHISM (ii) ENGINEERING

06

c) A company hires 11 new employees, each of whom is to be assigned to one of four

subdivisions. Each subdivision will get atleast one new employee. In how many ways can

these assignments be made?

06

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USN: 4 M C



Course Title : Finite Automata & Formal Language Course Code : IS 502






PART – A

1. a) Define finite automata. What are the applications of finite automata? 05

b) If D is the DFA constructed from NFA N by the subset construction, prove that L(D) = L(N). 07

c) Convert the following NFA to a DFA.

08

2. a) Prove that a language L is accepted by some -NFA if and only if L is accepted by some

DFA.

05

b) Define regular expression. Obtain a regular expression for the set of all strings of 0’s and 1’s

that do not end with 01 over ={0, 1}.

05

c) Write a DFA to accept all strings of 0’s and 1’s that have atleast one 0. Obtain a regular

expression for the same DFA.

10

PART – B

3. a) Prove that the language L={0n1n| n 1} is not regular. 05

b) Consider the following DFAs:

Prove that the intersection of the two regular languages represented by the two DFAs is also a

regular language.

05

c) Draw the table of distinguishabilities and obtain the minimum state equivalent DFA for the

following DFA.

10

P.T.O.

IS 502

4. a) Obtain a context free grammar to generate the language L = { | na() > nb()}. 05

b) Obtain the leftmost and rightmost derivation for the string aaabbabbba using the following

grammar:

S aB|bA

A aS|bAA|a

B bS| aBB|b

05

c) What is ambiguous grammar? Obtain the unambiguous grammar for the following ambiguous

grammar.

E E+E|E-E

E E*E|E/E

E (E)| I

I a|b|c

05

d) Write a short note on applications of CFGs. 05

PART – C

5. a) Obtain a PDA to accept the language L={R | t (a, b)*}. Show the sequence of moves

made by the PDA for the string 11000011.

08

b) Convert the following grammar to a PDA.

I a|b|Ia|Ib|I0|I1

E I|EE|E+E|(E)

05

c) Eliminate useless symbols, -productions and unit productions from the following grammar

and put it into CNF.

S 0A0| 1B1 | BB

A C

B S|A

C S|

07

6. a) Prove that if L is a CFL and R is a regular language, then LR is a CFL. 05

b) Explain the working of a turing machine. 05

c) Design a turing machine to accept the language L = { | (0+1)*} containing the substring

001. draw the transition diagram and show the IDs of the TM for the string 101001.

10

PART – D

7. a) Design a turing machine to accept the language 01* + 10* i.e., the TM remembers in its finite

control the first symbol (0 or 1) that it sees, and checks that it does not appear elsewhere on its

input.

08

b) What are multitape turing machines? Show the simulation of a two-tape turing machine by a

one-tape turing machine.

07

c) Write a short note on restricted turing machines. 05

8. a) Explain how a computer can simulate a turing machine. 05

b) What is universal turing machine? Explain the organization and operation of a universal truing

machine.

09

c) Define Post’s correspondence problem. Determine whether the following PCP instance has a

solution or not.

06

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USN: 4 M C



Course Title : File Structures Course Code : IS 503






PART – A

1. a) What are general goals of research and development in file structures? 04

b) Explain journey of a byte from memory to disk. 10

c) Write a C program to read stream of characters from file and display it on the screen. 06

2. a) List and explain different ways of adding structure to a file to maintain the identity of records?

Give example.

10

b) List and explain different classes to manipulate buffers. 10

PART – B

3. a) Define data compression. Explain suppressing repeating sequence technique with example. 07

b) Explain key-sorting technique and list their limitation. 08

c) Write a note on storage fragmentation. 05

4. a) What is an index? Explain the operations required to maintain the index files. 08

b) Explain the use of inverted list with its advantages. 06

c) Write a note on binding. 06

PART – C

5. a) Write algorithm to match names in two list. Also list the components that have to be dealt to

make match algorithm work fine.

08

b) Write heap sort algorithm. Construct heap for keys F, D, C, G, H, I, B, E, A. 08

c) Explain k-way merging. 04

6. a) Define a B-tree. Explain the creation of a B-tree with example. 10

b) What are AVL trees? List their properties. 04

c) What are paged binary tree? Explain their problems. 06

PART – D

7. a) Explain deletion, merging and redistribution of elements in a B-tree. 10

b) Compare strength and weakness of B+trees and B-tree. 04

c) Write a note on (i) LRU replacement (ii) Replacement based on page height. 06

8. a) Define hashing? Explain simple hashing algorithm. 10

b) Explain how extendible hashing works with neat diagram. 10

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USN: 4 M C



Course Title : Database Management Systems Course Code : IS 504






PART – A

1. a) What is a database? What are the properties of a database? 05

b) What is DBMS? Give an example. 05

c) What are the advantages of using the DBMS approach? Explain. 10

2. a) List and explain different types of attributes of the database with example. 05

b) Explain how role names are assigned in case of recursive relationship? Illustrate with a

example design.

05

c) List and explain all the notations of ER diagrams. 10

PART – B

3. a) Discuss the characteristics of relations. 05

b) What are the constraints on databases? Explain. 05

c) List the operations of relational algebra and purpose of each. 10

4. a) Explain the relational database design using ER-to-Relational mapping. 10

b) Write queries for the following:

i) Retrieve the name and address of all employees who work for the ‘Research’

department.

ii) List the names of all employees with two or more dependents.

10

PART – C

5. a) Write SQL queries for the following

i) Find the sum of the salaries of all employees, the maximum salary, the minimum

salary and the average salary.

ii) For each project, retrieve the project number, the project name and the number of

employees who work on that project.

iii) Retrieve the social security numbers of all employees who work on project

numbers 1, 2 or 3.

10

b) What are the features of SQL? 05

c) In which circumstances the stored procedures are useful? 05

6. a) Discuss the four informal design guidelines for relation schemes. 10

b) What are the inference rules for functional dependencies? 10

P.T.O.

IS 504

PART – D

7. a) What are the conditions to be satisfied for minimal sets of functional dependencies? 06

b) Give definitions of 2NF, 3NF and BCNF. 06

c) What are ACID properties? Explain. 08

8. a) Briefly discuss the two phase locking protocol used in concurrency control. 10

b) Write note on:

i) Serializability

ii) ARIES

iii) Write-ahead log protocol

iv) Crash recovery.

10

V

USN: 4 M C



Course Title : Computer Networks-I Course Code : IS 505






PART – A

1. a) What are the fundamental characteristics of Data Communication? What criteria must a

Communication network meet?

05

b) For n devices in a network, what is the number of cable links required for mesh, star, ring, and

bus topologies? Which of these is most secure?

05

c) Why is layered architecture preferable? Explain the function of Data Link Layer. 05

d) Describe the addresses used in an internet. 05

2. a) What is meant by Baseband and Broadband transmissions? If the power of a signal reduces to

half of its original value, calculate the attenuation in dB.

05

b) There is a channel with 4 KHz bandwidth. If we want to send data at 100 kbps, what is the

minimum SNR? What is SNRdb (correct to 2 decimal places)? What are the causes for

transmission impairments?

05

c) Why is Line coding necessary? What are the desirable features of line coding schemes? 05

d) Draw the graph of the signal for the data stream 10011 encoded using:

i) Unipolar NRZ (ii) NRZ-L (iii) Manchester (iv) Differential Manchester

v) AMI schemes.

05

PART – B

3. a) What is Scrambling? Explain one technique for the same. 05

b) Briefly explain Pulse Code Modulation. 05

c) Why is digital-to-analog signal conversion necessary? Compare ASK and FSK. 05

d) What is a QPSK? Show BPSK and QPSK by constellation diagrams. 05

4. a) What is multiplexing? What is its advantage? Five channels, each with a 100 KHz bandwidth,

are to be frequency multiplexed together with a guard band of 10 KHz between the channels.

What is the minimum bandwidth of the link required?

05

b) Four sources, each creating 250 characters per second are time division multiplexed. If the

interleaved unit is a character and 1 synchronizing bit is added to each frame, find (i) The data

rate of each source (ii) The duration of each character in each source (iii) The duration of

each frame, (iv) The number of bits in each frame and (v) The data rate of the link.

05

c) Derive the data rate of the T1 Line/ Carrier. Briefly explain direct sequence spread spectrum

technique.

05

d) What are the advantage of optical fiber communication? What are Single-mode and

Multi-mode fibres?

05

PART – C

5. a) Compare Datagram network and virtual Circuit Network. 05

P.T.O.

IS 505

b) Find the total number of cross points in a three-stage, 200x200 non-blocking switch (Use

Clos criterion)

05

c) Write an 8x8 Banyan switch and show routing from port 1 to port 6. 05

d) What is DSL technology? What is ADSL? Explain DMT. 05

6. a) What is the error detecting capability of Parity Check Code? How is this improved by two-

dimensional parity check?

05

b) Calculate the (7, 4) Hamming codeword for the dataword 1110. 05

c) Calculate the CRC codeword to be transmitted for a dataword: 1110 using the generator

polynomial g(x) = x3 + x + 1.

05

d) Calculate the internet checksum for the hexadecimal words 466F, 726F, 757A, 616E. 05

PART – D

7. a) Construct the frame for the data with characters below. What is Flow control?

A B ESC C ESC Flag

05

b) What is the maximum size of the send window in Go-Back-N ARQ Protocol? Why? 05

c) Describe the I-frame used in HDLC? 05

d) Explain the Challenge Handshake Authentication Protocol (CHAP) used in PPP. 05

8. a) Explain the SONET connections with a diagram. What is the data rate of STS-1 signal? 05

b) Describe the STS-1 Frame format. 05

c) What is Frame relay? What are the features? 05

d) What problems existed before the advent of ATM networks? How does ATM solve them? 05

V

USN: 4 M C



Course Title : Java & J2EE Course Code : IS 506






PART – A

1. a) Briefly explain any six key considerations used for designing java language? 06

b) Explain the process of building & running java application program with a neat flowchart? 08

c) Write a program to calculate the average among the elements i.e {8, 4, 5, 6, 7} using enhanced

for loop.

06

2. a) Which is the alternative approach to implement multiple inheritance in java? Explain with an

example.

06

b) What is exception? Write a program which contains a method called Throw ( ), which will

throw Illegal Access Exception & use proper exception handlers so that exception should be

printed.

08

c) What is an applet? Write a applet program that set the background color to cyan & foreground

color to pink & output the message “A simple applet program”.

06

PART – B

3. a) Write a java program, which creates two threads, one thread display “MALNAD COLLEGE

OF ENGIENERING’ for every 100 seconds & another thread display “Karnataka” for every

50 second continuously.

06

b) Explain the read-write problem with example. 06

c) Define the Delegation event model. Briefly explain the role of

i) Adapter classes (ii) Inner class (iii) Event class.

08

4. a) Explain any six components of the swing package. 06

b) List four types of buttons in swing with their uses. 04

c) Write a swing applet program that has two buttons named “Alpha” & “Beta”. When either of

the buttons pressed, it should display “Alpha is pressed” & “ Beta” is pressed” respectively.

10

PART – C

5. a) Describe the various steps of JDBC process, with code snippets. 10

b) What is transaction processing? Write a program to execute database transaction. 10

6. a) What is Servlet? Explain the life cycle of the Servlet. 06

b) Write a program using Servlet which read a parameter from webpage, say value1, which are

of type integer & find the area of circle & return back the result as a webpage.

10

c) Explain the role of (i) Cookies (ii) Session tracking 04

P.T.O.

IS 506

PART – D

7. a) What is JSP? Explain the different JSP tag’s with syntax. 06

b) Write a JSP program to create & read cookie named USERID that store’s the value “IS506”. 08

c) Describe code snippet & RMI at server side. 06

8. a) Explain the various EJB transaction attributes? 08

b) Write a note on

i) Session java bean (ii) Entity java bean (iii) Deployment descriptors.

12

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