GATE Exam Question Paper Question paper

Questions And Answers

No. Question

1 The availability of a complex software is 90%. Its Mean Time Between Failure (MTBF) is 200 days. Because of the critical nature of the usage, the organization deploying the software further enhanced it to obtain an availability of 95%. In the process, the Mean Time To Repair (MTTR) increased by 5 days.

What is the MTBF of the enhanced software

Options

A) 205 days B) 300 days

C) 500 days D) 700 days

Correct Answer C

2 A line L in a circuit is said to have a stuck-at-0 fault if the line permanently has a logic value 0. Similarly a line L in a circuit is said to have a stuck-at-1 fault if the line permanently has a logic value 1. A circuit is said to have a multiple stuck-at fault if one or more lines have stuck at faults. The total number of distinct multiple stuck-at faults possible in a circuit with N lines is

Options

A) 3N B) 3N-1

C) 2N-1 D) 2N

Correct Answer C

3 Which of the following statements is TRUE about the regular expression 01*0?

Options

A) It represents a finite set of finite strings. B) It represents an infinite set of finite strings.

C) It represents a finite set of infinite strings. D) It represents an infinite set of infinite strings.

Correct Answer B

4 In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?

Options

A)

3

23

B)

6

23

C)

3

10

D)

3

5

Correct Answer B

5 We have two designs D1 and D2 for a synchronous pipeline processor. D1 has 5 pipeline stages with execution times of 3 nsec, 2 nsec, 4 nsec, 2 nsec and 3 nsec while the design D2 has 8 pipeline stages each with 2 nsec execution time. How much time can be saved using design D2 over design D1 for executing 100 instructions?

Options

A) 214 nsec B) 202 nsec

C) 86 nsec D) -200 nsec

Correct Answer A

6 The numbers 1, 2,.... n are inserted in a binary search tree in some order. In the resulting tree, the right subtree of the root contains p nodes. The first number to be inserted in the tree must be

Options

A) p B) p + 1

C) n - p D) n - p + 1

Correct Answer D

7 In a computer system, four files of size 11050 bytes, 4990 bytes, 5170 bytes and 12640 bytes need to be stored. For storing these files on disk, we can use either 100 byte disk blocks or 200 byte disk blocks (but can't mix block sizes). For each block used to store a file, 4 bytes of bookkeeping information also needs to be stored on the disk. Thus, the total space used to store a file is the sum of the space taken to store the file and the space taken to store the bookkeeping information for the blocks allocated for storing the file. A disk block can store either book keeping information for a file or data from a file, but not both.

What is the total space required for storing the files using 100 byte disk blocks and 200 byte disk blocks respectively?

Options

A) 35400 and 35800 bytes B) 35800 and 35400 bytes

C) 35600 and 35400 bytes D) 35400 and 35600 bytes

Correct Answer C

8 Which of the following commands or sequences of commands will rename a file x to file y in a Unix system ?

I. mv y, x

II. mv x, y

III. cp y, x (rm x)

IV. cp x, y (rm x)

Options

A) II and III B) II and IV

C) I and III D) II only

Correct Answer B

9 Let n = p2q, where p and q are distinct, prime numbers. How many numbers m satisfy 1 £ m £ n and gcd (m, n) = 1? Note that gcd (m, n) is the greatest common divisor of m and n.

Options

A) p(q - 1) B) pq

C) (p2 - 1) (q - 1) D) p(p - 1) (q - 1)

Correct Answer D

10 Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for any two subsets S1 and S2 in C, either S1 Ì S2 or S2 Ì S1. What is the maximum cardinality of C?

Options

A) n B) n + 1

C) 2n-1+ 1 D) n!

Correct Answer C

11

Consider two tables in a relational database with columns and rows as follows:

Table: Student Table: Department

Roll_no Name Dept_id Dept_id Dept_name

1 ABC 1 1 A

2 DEF 1 2 B

3 GHI 2 3 C

4 JKL 3

Roll_no is the primary key of the Student table, Dept_id is the primary hey of the Department table and Student. Dept_id is a foreign key from Department. Dept_id What will happen if we try to execute the following two SQL statements?

(i) update Student set Dept_id = Null where Roll_on = 1

(ii) update Department set Dept_id = Null where Dept_id = 1

Options

A) Both (i) and (ii) will fail

B) (i) will fail but (ii) will succeed

C) (i) will succeed but (ii) will fail

D) Both (i) and (ii) will succeed

Correct Answer B

12 Let M = (K, å , G, D, s, F) be a pushdown automaton, where

K = {s, f}, F = {f}, å = {a, b}, G = {a} and

D = {((s, a, e), (s, a)), ((s, b, e), (s, a)), (( s, a, e), (f, e)), ((f, a, a ), (f, e)), ((f, b, a), (f, e))}

Which one of the following strings is not a member of L(M)?

Options

A) aaa B) aabab

C) baaba D) bab

Correct Answer C

13 Let P be a non-deterministic push-down automaton (NPDA) with exactly one state, q, and exactly one symbol, Z, in its stack alphabet. State q is both the starting as well as the accepting state of the PDA. The stack is initialized with one Z before the start of the operation of the PDA. Let the input alphabet of the PDA be å . Let L(P) be the language accepted by the PDA by reading a string and reaching its accepting state. Let N(P) be the language accepted by the PDA by reading a string and emptying its stack.

Which of the following statements is TRUE?

Options

A) L(P) is necessarily å * but N(P) is not necessarily å*. B) N(P) is necessarily å* but L(P) is not necessarily å*.

C) Both L(P) and N(P) is necessarily å*. D) Neither L(P) nor N(P) are necessarily å*.

Correct Answer D

14

Let p, q, r and s be four primitive statements. Consider the following arguments:

P: [(Ø p Ú q) Ù (r ® s) Ù (p Ú r)] ® (Øs ® q)

Q: [(Ø p Ú q) Ù (q ® (p ® r))] ® Ør

R: [((q Ù r) ® p) Ù (Øq Ú p)] ® r

S: [p Ù (p ® r) Ù (q Ú Ør)] ® q

Which of the above arguments are valid?

Options

A) P and Q only B) P and R only

C) P and S only D) P, Q, R and S

Correct Answer C

15 Assume that the delivered lines of code L of a software is related to the effort E in person months and duration t in calendar months by the relation L P* (E/B)1/3 * t4/3 , where P and B are two constants for the software process and skills factor. For a software project, the effort was estimated to be 20 person months and the duration was estimated to be 8 months. However, the customer asked the project team to complete the software project in 4 months. What would be the required effort in person months?

Options

A) 10 B) 40

C) 160 D) 320

Correct Answer D

16 Traceroute reports a possible route that is taken by packets moving from some host A to some other host B. Which of the following options represents the technique used by traceroute to identify these hosts

Options

A) By progressively querying routers about the next router on the path to B using ICMP packets, starting with the first router B) By requiring each router to append the address to the ICMP packet as it is forwarded to B. The list of all routers en-route to B is returned by B in an ICMP reply packet

C) By ensuring that an ICMP reply packet is returned to A by each router en-route to B, in the ascending order of their hop distance from A D) By locally computing the shortest path from A to B

Correct Answer C

17

Consider a list of recursive algorithms and a list of recurrence relations as shown below. Each recurrence relation corresponds to exactly one algorithm and is used to derive the time complexity of the alogrithm.

Recursive Algorithm Recurrence Relation

P. Binary search I. T(n) = T(n-k) + T(k) + cn

Q. Merge sort II. T(n) = 2T(n -1) + 1

R. Quick sort III. T(n) = 2T(n/2) + cn

S. Tower of Hanoi IV. T(n) = T(n/2) + 1

Which of the following is the correct match between the algorithms and their recurrence relations?

Options

A) P-II, Q-III, R-IV, S-I B) P-IV, Q-III, R-I, S-II

C) P-III, Q-II, R-IV, S-I D) P-IV, Q-II, R-I, S-III

Correct Answer B

18 A function f defined on stacks of integers satisfies the following properties.

f(f)= 0 and f(push(S, i)) = max (f(S),0) + i for all stacks S and integers i. If a stack S contains the integers 2, -3, 2, -1, 2 in order from, bottom to top, what is f(S)?

Options

A) 6 B) 4

C) 3 D) 2

Correct Answer C

19 Consider the following C program which is supposed to compute the transpose of a given 4x4 matrix M. Note that, there is an X in the program which indicates some missing statements. Choose the correct option to replace X in the program.

#include

#define ROW 4

#defme COL 4

int M[ROW][COL] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16};

main( )

{

int i, j, t;

for (i=0; i<4; ++i)

{

X

}

for (i=0; i<4; ++i) for (j=0; j<4; ++j)

printf("%d", M[j]);

}

Options

A) for(j=0; j<4; ++j){

t = M[j];

M[j] = M[j];

M[j] = t;

} B) for(j=0; j<4; ++j){

M[j] = t;

t = M[j];

M|j] = M[j];

}

C) for(j=i; j<4; ++j){

t = M[j];

M[j] = M[j];

M[j] = t;

} D) for(j=i; j<4; ++j]){

M[j] = t;

t = M[j];

M[j] = M[j];

}

Correct Answer C

20

Consider the following program module:

int module1 (int x, int y)

while (x!=y) {

if(x > y)

x = x - y;

else y = y - x;

}

return x;

}

What is Cyclomatic complexity of the above module?

Options

A) 1 B) 2

C) 3 D) 4

Correct Answer C