## GATE SAMPLE QUESTION PAPER-COMUTER SCIENCE

onsider the following program segment for a hypothetical CPU having three user registers Rl, R2 and R3.

Instruction Operation Instruction Size (in words)

MOV Rl,5000 ; Rl ¬ Memory[5000] 2

MOV R2,(R1) ; R2 ¬ Memory[(Rl)] 1

ADD R2,R3 ; R2 ¬ R2 + R3 1

MOV 6000, R2 ; Memory[6000] ¬ R2 2

HALT ; Machine halts 1

Let the clock cycles required for various operations be as follows:

Register to/from memory transfer : 3 clock cycles

ADD with both operands in register : 1 clock cycle

Instruction fetch and decode : 2 clock cycles per word

The total number of clock cycles required to execute the program is

Options

A) 29 B) 24

C) 23 D) 20

Correct Answer B

2 The order of an internal node in a B+ tree index is the maximum number of children it can have. Suppose that a child pointer takes 6 bytes, the search field value takes 14 bytes, and the block size is 512 bytes. What is the order of the internal node?

Options

A) 24 B) 25

C) 26 D) 27

Correct Answer C

3 The Boolean function x, y, + xy + x, y

Options

A) x, + y, B) x + y

C) x + y, D) x, + y

Correct Answer D

4 In an MxN matrix such that all non-zero entries are covered in a rows and b columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is

Options

A) £ a + b B) £ max {a, b}

C) £ min {M-a, N-b} D) £ min {a, b}

Correct Answer A

5 The relation scheme Student Performance (name, courseNo, rollNo, grade) has the following functional dependencies:

name, courseNo ® grade

rollNo, courseNo ® grade

name ® rollNo

rollNo ® name

The highest normal form of this relation scheme is

Correct Answer A

6 The minimum number of page frames that must be allocated to a running process in a virtual memory environment is determined by

Options

A) the instruction set architecture B) page size

C) physical memory size D) number of processes in memory

Correct Answer D

7

Consider the following program segment for a hypothetical CPU having three user registers Rl, R2 and R3.

Instruction Operation Instruction Size (in words)

MOV Rl,5000 ; Rl ¬ Memory[5000] 2

MOV R2,(R1) ; R2 ¬ Memory[(Rl)] 1

ADD R2,R3 ; R2 ¬ R2 + R3 1

MOV 6000, R2 ; Memory[6000] ¬ R2 2

HALT ; Machine halts 1

Consider that the memory is byte addressable with size 32 bits, and the program has been loaded starting from memory location 1000 (decimal). If an interrupt occurs while the CPU has been halted after executing the HALT instruction, the return address (in decimal) saved in the stack will be

Options

A) 1007 B) 1020

C) 1024 D) 1028

Correct Answer A

8 Let G be a simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of G is 8. Then, the size of the maximum independent set of G is

Options

A) 12 B) 8

C) Less than 8 D) More than 12

Correct Answer A

9 What does the following algorithm approximate? (Assume m > 1, Î > 0).

x = m;

y-i;

while (x – y > Î)

{ x = (x + y) / 2 ;

y = m/x ;

}

print (x) ;

Options

A) log m B)

m2

C) m1/2 D) m1/3

Correct Answer C

10 Consider the following C program

main ()

{ int x, y, m, n ;

scanf (“%d %d”, &x, &y);

/ * Assume x > 0 and y > 0 * /

m = x; n = y ;

while ( m ! = n)

{ if (m > n)

m = m — n;

else

n = n – m ; }

printf(“%d”,n); }

The program computes

Options

A) x + y, using repeated subtraction

B) x mod y using repeated subtraction

C) the greatest common divisor of x and y

D) the least common multiple of x and y

Correct Answer C

11 The best data structure to check whether an arithmetic expression has balanced parentheses is a

Options

A) queue B) stack

C) tree D) list

Correct Answer B

12 A Priority-Queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is given below:

10, 8,5,3,2

Two new elements 1 and 7 are inserted in the heap in that order. The level-order traversal of the heap after the insertion of the elements is

Options

A) 10,8,7,5,3,2,1 B) 10,8,7,2,3,1,5

C) 10,8,7,1,2,3,5 D) 10,8,7,3,2,1,5

Correct Answer D

13

Consider the following C program segment

struct CellNode {

struct CellNode *leftChild ;

int element;

struct CellNode *rightChild ;

};

int DoSomething (struct CellNode *ptr)

{

int value = 0 ; if (ptr ! = NULL)

{ if (ptr->leftChild ! = NULL)

value = 1 + DoSomething (ptr – > leftChild) ;

if (ptr – > rightChild ! = NULL)

value = max (value, 1 + DoSomething (ptr – > rightChild)) ;

}

return (value);

}

The value returned by the function DoSomething when a pointer to the root of a

non-empty tree is passed as argument is

Options

A) The number of leaf nodes in the tree

B) The number of nodes in the tree

C) The number of internal nodes in the tree D) The height of the tree

Correct Answer D

14 An organization has a class B network and wishes to form subnets for 64 departments. The subnet mask would be

Options

A) 255.255.0.0 B) 255.255.64.0

C) 255.255.128.0 D) 255.255.252.0

Correct Answer D

15 Suppose the round trip propagation delay for a 10 Mbps Ethernet having 48-bit jamming signal is 46.4 ms. The minimum frame size is:

Options

A) 94 B) 416

C) 464 D) 512

Correct Answer C

16

Consider the following C program segment:

char p [ 20];

char * s = “string” ;

int length = strlen (s) ;

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

p[ i ] = s [length – i] ;

print f (“%s”, p) ;

The output of the program is

Correct Answer A

17 Consider the grammar

S ® (S) | a

Let the number of states in SLR(1), LR(1) and LALR(1) parsers for the grammar be n1, n2 and n3 respectively. The following relationship holds good

Options

A) n1< n2 < n3 B) n1= n3 < n2

C) n1= n2 = n3 D) n1 ³ n3 ³ n2

Correct Answer B

18 Consider the following C function:

int f (int n)

{ static int i = 1;

if (n >= 5) return n;

n = n + i;

i ++;

return f (n);

}

The value returned by f(1) is

Options

A) 5 B) 6

C) 7 D) 8

Correct Answer C

19 Consider the following code fragment:

if (fork ( ) = = 0)

{a = a + 5; print f (“%d, %d / n”, a, and a); }

else {a – 5; print f (“ %d, %d / n”, a,& a); }

Let u, v be the values printed by the parent process, and x, y be the values printed by the child process. Which one of the following is TRUE?

Options

A) u = x + 10 and v = y B) u = x + 10 and v ¹ y

C) u + 10 =x and v = y D) u + 10 = x and v ¹ y

Correct Answer B

20 The following numbers are inserted into an empty binary search tree in the given order: 10, 1, 3, 5, 15, 12, 16. What is the height of the binary search tree (the height is the maximum distance of a leaf node from the root)?

Options

A) 2 B) 3

C) 4 D) 6

Correct Answer B

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