GATE Question Papers: Computer Science and Engineering 2008

Q.1 – Q.20 Carry One Mark Each

1. equals

(A) 1 (B) -1 (C) ¥ (D) - ¥

2. If P, Q, R are subsets of the universal set U, then

(P Ç Q Ç R) È (P^c Ç Q Ç R) È Q^c È R^c is

(A) Q^c È R^c (B) P È Q^c È R^c (C) P^c È Q^c È R^c (D) U

3. The following system of equations

has a unique solution. The only possible value(s) for a is/are

(A) 0 (B) either 0 or 1

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

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)

6. Let r denote number system radix. The only value(s) of r that satisfy the equation is / are

(A) decimal 10 (B) decimal 11

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) Q(n) (B) Q(m) (C) Q(m+n) (D) Q(mn)

8. Given f₁, f₃ and f in canonical sum of products form (in decimal) for the circuit

f₁ = åm (4, 5, 6, 7, 8)

f₃ = åm (1, 6, 15)

f = åm (1, 6, 8, 15)

then f₂ is

(A) å m (4, 6) (B) åm (4, 8) (C) åm (6, 8) (D) åm (4, 6, 8)

9. Which of the following is true for the language {a^p | p is a prime}?

(A) It is not accepted by a Turing Machine

(B) It is regular but not context-free

(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

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

(D) The information from the front end cannot otherwise be used for optimization

13. If L and are recursively enumerable then L is

(A) regular (B) context-free

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

15. Which of the following tuple relational calculus expression(s) is/are equivalent to

I. Ø$t Î r(P(t))

II. $t Ï r (P(t))

III. Ø$t Î r(ØP(t))

IV. $t Ï r (ØP(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

17. Which of the following system calls results in the sending of SYN packets?

(A) socket (B) bind

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

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) QMNPR O (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

(D) an extension of indexed allocation

Q.21 – Q.75 Carry Two Marks Each

21. The minimum number of equal length subintervals needed to approximate to an accuracy of at least ´ 10^-⁶using the trapezoidal rule is

(A) 1000e (B) 1000 (C) 100e (D) 100

22. The Newton-Raphson iteration can be used to compute the

(A) square of R (B) reciprocal 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

(D) The graph has an independent set of size at least n/3

24. Let P = and Q = where k is a positive integer. Then

(A) P = Q - K (B) P = Q + K (C) P = Q (D) P = Q + 2K

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 3x⁴ - 16x³ + 24x² + 37 is

(A) 0 (B) 1 (C) 2 (D) 3

26. If P, Q, R are Boolean variables, then

Simplifies to

(A) P. (B) P. (C) P.+ R (D) P.+ 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?

and

(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 ³ 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)) Þ ($y pda(y) Ù equivalent (x,y))

(B) ~ "y ($x fsa(x) Þ pda(y) Ù equivalent (x, y))

(D) "x $y (fsa(y) Ù pda(x) Ù equivalent (x, y))

31. P and Q are two propositions. Which of the following logical expressions are equivalent?

I. P Ú ~ Q

II. ~ (~ P Ù Q)

III. (P Ù Q) Ú (P Ù ~ Q) Ú (~ P Ù ~ Q)

IV. (P Ù Q) Ú (P Ù ~ Q) Ú (~ P Ù Q)

(A) Only I and II (B) Only I, II and III

32. For a magnetic disk with concentric circular tracks, the seek latency is not linearly proportional to the seek distance due t o

(A) non-uniform distribution of requests

(B) arm starting and stopping inertia

(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

(A) I only (B) II only (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

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

(D) After data cache lookup has completed

39. Consider the following functions:

f(n) = 2ⁿ

g(n) = n!

h(n) = n^logn

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) = W(g(n)); g(n) = O(h(n))

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) Q(n) (B) Q(logn) (C) Q(log*n) (D) Q(1)

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

(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

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

(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

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) Q(logn)

(B) Q(n)

(D) None of the above, as the tree cannot be uniquely determined

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) Q(log n) (B) Q(n) (C) Q(n log n) (D) Q(n²)

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

(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)

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 e-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

51. Match the following:

E.	Checking that identifiers are declared before their use	P.	L = {aⁿb^mcⁿd^m\|n ³ 1, m ³ 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\|wÎ(a\|b)*}\|
H.	Palindromes	S.	X ® bXb \| cXc \| e

(A) E - P, F - R, G - Q, H - S (B) E - R, F - P, G - S, H - Q

52. Match the following NFAs with the regular expressions they correspond to

1. e + 0(01*1 + 00) * 01*

2. e + 0(10 *1 + 00) * 0

3. e + 0(10 *1 + 10) *1

4. e + 0(10 *1 + 10) *10 *

(A) P - 2, Q - 1, R - 3, S - 4 (B) P - 1, Q - 3, R - 2, S - 4

53. Which of the following are regular sets?

I. {aⁿb^2m|n ³ 0, m ³ 0}

II. {aⁿb^m|n = 2m}

III. {aⁿb^m|n ¹ m}

IV. {xcy|x, y, Î {a, b} *}

(A) I and IV only (B) I and III 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

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

(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

57. If a class B network on the Internet has a subnet mask of 255.255.248.0, what is the maximum number of host s per subnet?

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

(D) connect () system call results in a core dump

60. What is printed by the following C program?

{ {

int y, z; int c, *b, **a;

**ppz + = 1; z = *ppz; c = 4; b = &c; a = &b;

*py + = 2; y = *py; print 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 ();

}

main () {

print f ("Enter Text"); print f ("\ n");

reverse (); print f ("\ n");

}

(A) ?1 is (getchar ( )! = '\ n')

?2 is getchar (c);

(B) ?1 is (c = getchar ( ) )! = '\ n')

?2 is getchar (c);

?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;

if s < 0 then wait;

V(s) : s = s + 1;

if s <= 0 then wakeup a process waiting on s;

Assume that P_b and V_b the wait and signal operations on binary semaphores are provided. Two binary semaphores x_b and y_b are used to implement the semaphore operations P(s) and V(s) as follows:

P(s) : P_b (x_b);

s = s -1;

if (s < 0) {

V_b (x_b);

P_b (y_b);

}

else V_b (x_b);

V(s) : P_b (x_b);

s = s + 1;

if (s <=0) V_b (y_b);

V_b (x_b);

The initial values of x_b and y_b 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

(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) 2ⁿ - 1 (C) 2ⁿ (D) 2ⁿ⁺¹ - 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

68. Let R and S be two relations with the following schema

R ()

S ()

Where {P, Q} is the key for both schemas. Which of the following queries are equivalent?

I. Õ_p (R S)

II. Õ_p (R) Õ_p (S)

III. Õ_p (Õ_{p, Q} (R) Ç Õ_p,
Q (S))

IV. Õ_p (Õ_{p, Q} (R) - (Õ_p,
Q (R) - Õ_{p, Q
(S)))}

(A) Only I and II (B) Only I and III

69. Consider the following relational schemes for a library database:

Book (Title, Author, Catalog_no, Publisher, Year, Price)

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 ® Price

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

(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

(A) 8 and 0 (B) 128 and 6 (C) 256 and 4 (D) 512 and 5

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) Q (n) and Q (n) (B) Q (2ⁿ) and Q (n)

75. F1 (8) and f2 (8) return the values

(A) 1661 and 1640 (B) 59 and 59

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

(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

Statement for Linked Answer Questions: 78 & 79

Let x_n denote the number of binary strings of length n that contain no consecutive 0s.

78. Which of the following recurrences does x satisfy?

(A) x_n = 2x_n_-₁ (B) x_n = + 1

79. The value of x₅ is

(A) 5 (B) 7 (C) 8 (D) 16

Statement for Linked Answer Questions: 80 & 81

The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a₁, a₂, a₃, ..., a_n}, 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 £ 0 £ j £ W, is TRUE if and only if there is a subset of {a₁, a₂, ... a_i} whose elements sum to j.

80. Which of the following is valid for 2 £ i £ n and a_i £ j £ W?

(A) X[i, j] = X[i - 1, j] Ú X[i, j - a_i] (B) X[i, j] = X[i - 1, j] Ú X[i - 1, j -a_i]

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]

Statement for Linked Answer Questions: 82 & 83

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}

Statement for Linked Answer Questions: 84 & 85

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) print f ("x is in the array");

9. else print f ("x is not in the array");

10. }

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

(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;

(D) Change line 7 to:} while ((Y[k] == x) && (i < j));

End of Question Paper