cs09 s3 qb

Question Bank 2009 Scheme Third Semester CSE

QUESTION BANK

III SEMESTER BTECH

DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING

JAWAHARLAL COLLEGE OF ENGINEERING AND TECHNOLOGY

Jawahar Gardens, Magalam, Lakkidi-Perur, Ottapalam,Palakkad,Kerala.

2012


EN 09 301 ENGINEERING MATHEMATICS III

PART A

1. Define an analytic function and Entire function.

2. Show that is analytic and find its derivative

3. Show that an analytic with constant real part is constant.

4. Show that an analytic function with constant imaginary part is constant.

5. Determine whether C-R conditions are satisfied for the function .

6. Verify whether is harmonic or not.

7. Define cross ratio.

8. Find the fixed points of the mapping .

9. Find the critical points of the transformation .

10. Define conformal mapping and isogonal mapping.

11. Express the residue of a function at an isolated singularity as a contour integral.

12. Define connected and simply connected region.

13. State Cauchys integral theorem.

14. Evaluate , where C is a unit circle

15. Define isolated singularity, pole, essential singularity and removable singularity.

16. Find the residue of at .

17. How do you define the linear span of vectors in a vectorspace.

18. Define linear dependence and independence.

19. Check whether the given vectors are linearly independent or not

(1, 5, 3) , (2, 4, 6) , (3, 9, 1)


(1, 2, 3) , (4, 5, 6) , (7, 8, 9).

20. If Show that is a subspace of V.

21. Define vectorspace , basis and dimension of a vectorspace , also define subspace.

22. Write down the complex fourier transform pair.

23. Prove that then .

24. If and is any real number

25. Define forier sine and cosine integral representation.

PART B

1. Find a function w such that is analytic given that .

2. Find the image of the semi infinite strip under the transformation

Show the region graphically.

3. Show that is not analytic at the origin.

4. If is an analytic function of z , prove that .

5. Determine the analytic function ,whose real part is .

6. Discuss the transformation is it conformal at the origin.

7. Show that is everywhere continuous but not analytic.

8. Prove that a bilinear transformation maps circles into circles.

9. Prove that is an analytic.

10. Verify Cauchys theorem for dz where C: .

11. Evaluate where C : .


12. Evaluate , where C :

13. Evaluate where C is a simple closed curve and the point a is

Inside C

Outside C

14. Find the nature and location of singularities of

15. Find the Taylors series expansion of about the point z=i

16. Evaluate where C is the circle .

17. Evaluate along the paths .

18. Find the value of where C:

19. Evaluate ,where C:

20. Evaluate the following integral , where C is the ellipse =1

21. Evaluate where C:

22. Obtain the taylors expansion of in powers of (z-1).

23. Calculate the residues of the function at

24. Evaluate where C:

25. Expand as Laurents series about

26. Show that the vectors generates and verify that

that the triangle inequality is satisfied by the vector .

27. Show that the vectors (4,3,-1),(2,-1,5),(-1,1,2) are linearly independent.express (5,15,2) as a linear

combination of above vectors.

28. Verify whether is an innerproduct in or not for


( .

29. Find a basis and dimension of the subspace in generated by (1,-1,2,4) ,(2,1,3,0),(1,2,-1,0)

30. Let W be the subspace of generated by the vectors (1,-2,5,-3), (2,3,1,-4), (3,8,-3,-5) Find a basis and

dimension of W

31. Show that the vectors in are Orthogonal

32. Find a vector orthogonal to

33. Show that is self reciprocal under the Fourier transform

34. Find the fourier transform of the function

35. Find the fourier cosine and sine integral representation of

PART C

36. Show that is differentiable except at find its derivative

37. Find the bilinear transformation which maps on to the points

Hence find the image of

38. Determine thee analytic function if given that

39. Find the invariant point of the transformation and prove that these two points together

with any points z and its image w, from a set four points having a constant cross ratio. What is this cross

ratio?

40. Show that the function is not regular at the origin although Cauchy Riemann equations are

satisfied

41. Find the bilinear transformation which maps the point in to the points Find

the image of the line under this transformation

42. Find the Laurents series expansion of the function valid in the region


43. Find the value of the taken counter clockwise around the circle

1) 2)

44. 69. Evaluate where C is the circle

45. Find the Laurents series expansion of in the region

46. Evaluate the following

1) where C is the circle

2)

47. Prove that

48. Evaluate using residue theorem

49. If where C is the ellipse . Find the values of

.

50. Evaluate the integral using Residue theorem where C:

51. By integrating around unit circle,evaluate

52. Prove that the set of vectors (1,1,-2),(2,1,0) and (2,-2,1) are linearly independent of each other

and express (3,-4,0) as a linear combination of the above set of vectors .

53. Let W be the subspace of R4 generated by the vectors (1,-2,5,-3), (2,3,1,-4) and (3,8,-3,-5) Find a basis

and dimension of W

54. Find an orthonormal basis of the subspace W of R5 spanned by (1,1,1,0,1), (1,0,0,-1,1) (3,1,1,-2,3)

,(0,2,1,1,-1).

55. Explain how will you find an orthonormal bsis from a given set of nonzero independent vectors

56. Show that the vectors (1,2,3),(0,1,2),(0,0,1) generates R3

57. For what value of k will the vector (1,-2,k) inR3 be a linear combination of the vectors (3,0,-2)

and(2,-1,5)

58. Find the coordinate of the vectors (2,1,-6)of R3 relative to the basis (1,1,2),(3,-1,0)&(2,0,-1)


59. Apply Gram-schmidh Orthogonalisation process to obtain an orthonormal basis for R3 From the basis

given by (3,0,4),(-1,0,7),(2,9,1)

60. Using Fourier transform of

Evaluate

61. Find the Fourier transform of and hence evaluate

62. Using Fourier integral prove that , x

63. Find the Fourier cosine and sine transform of

64. Find the Fourier transform of

65. Express the function as a fourier sine integral and hence evaluate

.


EN09 302- HUMANITIES AND COMMUNICATION SKILLS

Common for all branches


CS09 303- DATA STRUCTURES

PART - A (2 Marks)

1. What is meant by enumerated data type?

2. What is the difference between linear and non linear data structures?

3. What is meant by threaded binary tree?

4. What is meant by sequential search?

5. Explain external sorting

6. What is an expression tree?

7. What is meant by time complexity? Why do we need to analyze the time complexity of a

program?

8. Give the prefix expression of the expression :

(a-b)* (c + d)/ e+f.

9. What is time complexity to delete a node in double linked list?

10. What is AVL tree ?

11. Define Hash function.

12. What is time complexity to delete a node in singly linked list?

13. Define Minimum spanning tree.

14. Find the time complexity of binary search.

15. Worst ease, what is time complexity of quick sort.


PART - B (5 Marks)

1. Explain in detail about space &time complexity?

2. Explain different operations on stack.

3. Define a graph. What is meant by in-degree &out-degree of a vertex?

4. Explain the algorithm for deletion operation performed on circular queue.

5. Explain the steps to be followed in BFS.

6. What is an array? Explain the method of address calculation for two-dimensional array in row-

major order and column major order.

7. What is a priority queue? Give the uses of priority queue.

8. Explain the advantages of linked list over arrays.

9. What is meant by balance factor of AVL tree?

10. Explain binary search.

11. Explain minimum spanning tree.

12. List the different methods of representations of strings.

13. Explain how a postfix expression can be evaluated using stacks.

14. What is priority queue? Give the use of priority queue.

15. What are the advantages and disadvantages of linked representation of binary tree?

16. Define a graph. What is meant by in-degree and out-degree of a vertex?

17. What is external sorting? Give the need of external sorting techniques.

18. Write the sequence of steps to be followed in binary search method.

19. Explain the depth first search algorithm on a graph.

20. What is the use of hash functions? List various methods to construct hash function.

21. Explain quick sort with example.

22. Convert following infix expression into postfix expression and prefix expression. (A

B)* C + D / (E G).

23. Write down the algorithm for deletion operation performed on the circular queue.

24. A Binary tree T has 9 nodes. The in-order and pre-order traversals yield

the following sequence of nodes :

in-order :EACKFHDBG

pre-order:FAEKCDHGB

Draw Binary Tree.

25. Explain operations on queue.


PART - C (10 Marks)

1. Find MST of the graph through Kruskal's algorithm

2. Explain binary tree traversals

3. Write a short note on the following

(a) BST (b) AVL Tree (c) DFS (d) Dijikstra's algorithm

4. Explain selection sort & insertion-sort algorithm with Example

5. Sort the following array of elements through Heap sort .

25,37,48,11,12,92,85,57.

6. Explain selection sort & insertion-sort algorithm with Example

7. Explain how infix expression can be converted into postfix expression using stacks.

8. Explain quick sort algorithm with Example

9. Briefly explain the analysis of factorial function in C.

10. Write algorithm (i) to search an element in a singly linked list (ii) to delete an element in

a doubly linked list.

11. What is a binary tree? Explain various binary tree traversal algorithms.

12. What is a binary search tree? Give an example. Write the algorithm for insertion and

deletion in a binary search tree.

13. Explain the insertion and selection sort algorithms.

14. Explain searching linked list with an example.

15. Explain n2 sorting methods

16. What is heap? Write and explain heap son algorithm.Derive time complexity of heap sort

algorithm.

17. Write algorithm (i) to search an element in a BST (ii) to insert an element in a BST.

18. Explain minimum spanning tree algorithms.

19. Write short notes on (i) Stack (ii) Sparsh matrices (iii) Circular linked list and (iv) Dequeue.

20. Write an algorithm to insert an element in doubly linked list

21. Write an algorithm to implement queue using linked list.

22. Define a B-tree of order M. Build a B-tree by inserting records with following key

sequence, into an empty B-tree of order 4

a, g, f, b, k, d, h, m,j, e, s, i, r, x, c, l, n, t, n, p.

23. Write an algorithm to implement queue using linked list.

24. Write the recursive algorithm for quicksort. Apply the algorithm for following array of

elements. 25, 11, 57 48, 37, 12, 92, 85. (Show only first partition.)

25. Sort the following array of elements through HEAP SORT and merge sort. 25,

37, 48, 11, 12, 92, 57, 85. Show all the steps.


CS09 304- DISCRETE COMPUTATIONAL STRUCTURES

PART - A (2 Marks)

1. Define partially ordered set.

2. Define equivalence relation.

3. Give an example of a bijective map.

4. Explain Hasse diagram.

5. Define isomorphism of groups.

6. Prove that identity element in a group is unique.

7. Define a cycle group.

8. Define a group code.

9. Define PDNF.

10. Explain modus tollens

11. Explain conjunctive normal form.

12. Define tautology.

13. Solve T(n) = T(n-1)+1 , T(0)=1

14. Solve an+1 = an +1 , a0 =1

15. Find the generating function of the sequence 1, 2, 3, ............

16. Find the generating function of the sequence 1, -1, 1, -1, ..........


PART - B (5 Marks)

1. Prove that p q ~ ( ~p q )

2. Find the PDNF of ( ~p q ) ( q p )

3. Show that d can be derive d from the premises ( a b ) ( a c ) , ~ ( b c ) , d a

4. Prove that the premises p q , q r , s ~ r and p s are inconsistent.

5. If R and S are

relations on a set A represented by the matrix

MR = 0 1 0

1 1 1

1 0 0

Find the matrix that represents R S, R S

6. Show that I congruent mod S is an equivalence relation. Find the equivalence classes.

7. Draw the Hasse diagram for {2,4,8,3,6,110,12,25,32} with divides as order

8. Let S= {(1,2), (2,1) } be a relation on a set A= {1,2,3}. Find the minimum number of ordered

pairs to make it an equivalence relation.

9. Show that every cyclic group is abelian.

10. On Q + show that * defined by a*b = (a*b)/2 (a,b Q+ is an abelian group.

11. Show that Z6 = {0,1,2,3,4,5} is a group under +6 and not a group under 6

12. Show that Z5 = {[1],[2],[3],[4]} is a group under 5

13. Show the recurrence relation an 2an-1 = 3n

, a1=5

14. Solve : an+1 2an =5 a0=1

Ms = 0 1 0

1 1 1

1 0 0


PART - C (10 Marks)

1. Sate and prove Lagranges theorem.

2. Solve an+2+3an+1+2an=3n where a0=0 and a1=1

3. Solve an+1-an = 3n^2

- n where a0=3

4. Solve the recurrence relation an+2 - 4an+1 + 3an = n2 where a0=0, and a1=0.

5. Solve by generating function an+2 5an+1 + 6an = 36 where n 0 , a0=0 and a1=0

6. Solve by generating function an+1+4an+4an-1 = n-1 where a0=0,a1=1

7. Find the code words generated by the encoding function e : B2 B5 w.r.t

the parity check matrix H = 0 1 1

0 1 1

1 0 0

0 1 0

0 0 1

8. Show that from

x ( F(x) S(x) ) y ( M(y) W(y) )

y ( M(Y) ~ W(Y) ) y ( M(y) W(y) )

the conclusion is x ( F(x) ~ S(x) ) follows

9. If f: a H is a homomorphism and a G show that

a) f(a-1) =(f(a))-1

b) f(e) =e-1

c) if K is a subgroup of G then f(k) is a subgroup of H

10. Find PDNF and PCNF of (pq) (~pr) (qr )

11. Prove that the minimum weight of nonzero code words in a group code is the minimum

distance.


CS09 306- SWITCHING THEORY AND LOGIC DESIGN

PART A

1. Mention the characteristics of digital ICs

2. Write a short note on ASCII character code.

3. Explain the operation of SR flip flop with truth table

4. Explain about Moore state model.

5. What is meant by Modulo N counter?

6. Define binary logic?

7. Convert (634) 8 to binary

8. State the different classification of binary codes?

9. Find the excess -3 code and 9s complement of the number 40310

10. What are basic properties of Boolean algebra?

11. Reduce A(A + B)

12. What are the methods adopted to reduce Boolean function?

13. What are called dont care conditions?

14. What is an essential implicant?

15. What is binary decoder?

16. Define Flip flop.

17. What is the operation of RS flip-flop?

18. Define race around condition.

19. Give the comparison between combinational circuits and sequential circuits.

20. What is critical race?

21. Explain the types of faults?

22. What is meant by fault diagnosis?

23. Define essential prime implicants theorem.


PART B

1. Reduce the following expression using K-map and implement them in universal logic.

M(1,4,5,11,12,14).d(6,7,15)

2. Show how the function Y(A,B,C)=m(0,2,3,4,5,7) can be implemented using 3 to 8 binary decoder and an

OR gate.

3. Design a 3 bit positive edge triggered ripple down counter using JK flip flop.

4. Design a MOD 7 synchronous up counter using T Flip flop.

5. Generate the sequence 110010 using sequence generator.

6. Reduce AB + (AC)' + AB'C(AB + C)

7. Simplify the following expression Y = (A + B)(A + C' )(B' + C'

8. Prove that ABC + ABC' + AB'C + A'BC = AB + AC + BC

9. Define duality property.

10. Mention the important characteristics of digital ICs?

11. List basic types of programmable logic devices.

12. What is programmable logic array? How it differs from ROM?

13. Define shift registers and its types?.

14. Explain ring counter and Johnson counter.

15. Design a mod 6 asynchronous counter using JK flip flop.

16. Convert JK flip flop to SR flip flop and design the circuit.

17. Generate the sequence 111010 using sequence detector.

18. Define test generation.

19. Define the path sensitization method .

20. Explain the fault table method.


PART C

1.Obtain the minimal expression using tabular method

m(1,5,6,12,13,14)+d(2,4)

2.Obtain the minimal SOP expression for m(2,3,5,7,9,11,12,13,14,15) and implement it in NAND logic.

3.Design a conversion circuit for BCD to EXCESS-3 code.

4.Explain in detail about look ahead carry adder and binary parallel subtractor.

5.Explain in detail about SISO,SIPO,PISO,PIPO and Universal shift register.

6.Explain in detail about edge triggered master slave JK Flip flop.

7.Derive a circuit that realizes the FSM defined by the state assigned table in the following table using JK Flip

flop.

Present state

Next state

Output

Z

W=0 W=1

Y1 Y0 Y1 Y0 Y1 Y0

0

0

1

1

0

1

0

1

1

0

1

1

0

1

1

0

1

0

0

0

1

0

0

1

0

0

0

1

8.Design a sequence detector to detect the sequence 1101.Overlapping is allowed.

9. Obtain the canonical sum of products of the function Y = AB + ACD


10. Explain the working of BCD Ripple Counter with the help of state diagram and logic

diagram.

11. Design a logic circuit to convert the BCD code to Excess 3 code.

12.Design a sequential detector which produces an output 1 every time the input sequence 1011

is detected.

13. Explain in detail about serial in serial out shift register.

14.Detect the sequence 0010 using sequence detector.overlapping is allowed.

15.Explain in detail about Finite state machines and its types.

16.Design a circuit that converts a BCD code to GRAY code.

17.Draw and explain 1 to 8 multiplexer.

18. Explain PLA folding in detail with example.

19. Explain the following with an example.

(i) Fault table method

(ii) Path sensitization method

(iii) Boolean difference method.

20.Explain in detail about the different types of faults.

cs09 s3 qb

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