GATE 2010 Computer Science Question Paper

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Question

Let G=(V, E) be a graph. Define $\xi (G) = \overset{\sum}{d}\ I_d$ x d , where i_d is the number of vertices of degree d in G. If S and T are two different trees with $\xi (S) = \xi (T)$ , then

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Selected	Possible Answer

Question

Newton-Raphson method is used to compute a root of the equation x^2 - 13 = 0 with 3.5 as the initial value. The approximation after one iteration is

Possible Answers

Selected	Possible Answer
	3.575
	3.676
	3.667
	3.607

Question

What is the possible number of reflexive relations on a set of 5 elements?

Possible Answers

Selected	Possible Answer
	$2^{10}$
	$2^{15}$
	$2^{20}$
	$2^{25}$

Question

Consider the set S = $\left \{ 1, \omega , \omega^2 \right \}$ , where $\omega\ and\ \omega^2$ are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms

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Selected	Possible Answer
	A group
	A ring
	An integral domain
	A field

Question

What is the value of $\overset{lim}{n \rightarrow \infty}$ $\Bigg(1- \cfrac{1}{n} \Bigg)^{2n}$ ?

Possible Answers

Selected	Possible Answer

	$e^{-2}$
	$e^{-1/2}$

Question

The minterm expansion of f (P, Q, R) = PQ + $Q \bar R + P \bar R$ is

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Selected	Possible Answer

Question

A main memory unit with a capacity of 4 megabytes is built using 1M×1-bit DRAM chips. Each DRAM chip has 1K rows of cells with 1K cells in each row. The time taken for a single refresh operation is 100 nanoseconds. The time required to perform one refresh operation on all the cells in the memory unit is

Possible Answers

Selected	Possible Answer
	100 nanoseconds
	100* $2^{10}$ nanoseconds
	100* $2^{20}$ nanoseconds
	3200* $2^{20}$ nanoseconds

Question

P is a 16-bit signed integer. The 2’s complement representation of P is $(F87B)_{16}$ . The 2’s complement representation of 8*P is

Possible Answers

Selected	Possible Answer
	$(C3D8)_{16}$
	$(187B)_{16}$
	$(F878)_{16}$
	$(987B)_{16}$

Question

The Boolean expression for the output f of the multiplexer shown below is

Possible Answers

Selected	Possible Answer
	$\cfrac{}{P \oplus Q \oplus R}$
	$P \oplus Q \oplus R$

	$\cfrac{}{P + Q + R}$

Question

In a binary tree with n nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child?

Possible Answers

Selected	Possible Answer
	0
	1
	(n – 1) /2
	n-1

Question

What does the following program print?
#include < stdio.h >
void f (int *p, int * g) {
p = q;
* p = 2;
}
int i = 0, j = 1;
int main ( ) {
f (&i, & j);
pr int f( “%d %d \ n”, i, j) ;
return 0;
}

Possible Answers

Selected	Possible Answer
	2 2
	2 1
	0 1
	0 2

Question

Two alternative packages A and B are available for processing a database having 10^k records. Package A requires 0.0001 n^2 time units and package B requires $10nlog_{10} n$ time units to process n records. What is the smallest value of k for which package B will be preferred over A?

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Selected	Possible Answer
	12
	10
	6
	5

Question

Which data structure in a compiler is used for managing information about variables and their attributes?

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Selected	Possible Answer
	Abstract syntax tree
	Symbol table
	Semantic stack
	Parse table

Question

Which languages necessarily need heap allocation in the runtime environment?

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Selected	Possible Answer
	Those that support recursion
	Those that use dynamic scoping
	Those that allow dynamic data structures
	Those that use global variables

Question

One of the header fields in an IP datagram is the Time to Live (TTL) field. Which of the following statements best explains the need for this field?

Possible Answers

Selected	Possible Answer
	It can be used to prioritize packets
	It can be used to reduce delays
	It can be used to optimize throughput
	It can be used to prevent packet looping

Question

Which one of the following is not a client server application?

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Selected	Possible Answer
	Internet chat
	Web browsing
	E-mail
	Ping

Question

Let L1 be a recursive language. Let L2 and L3 be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?

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Selected	Possible Answer
	L2 – L1 is recursively enumerable
	L1 – L3 is recursively enumerable
	L2 $\cap$ L1 is recursively enumerable
	L2 $\cup$ L1 is recursively enumerable

Question

Consider a B^+ -tree in which the maximum number of keys in a node is 5. What is the minimum number of keys in any non-root node?

Possible Answers

Selected	Possible Answer
	1
	2
	3
	4

Question

A relational schema for a train reservation database is given below
Passenger (pid, pname, age)
Re servation (pid, cass, tid)

What pids are returned by the following SQL query for the above instance of the tables?
SELECT pid
FROM Re servation
WHERE class ‘AC’ AND
EXISTS (SELECT *
FROM Passenger
WHERE age > 65 AND
Passenger.pid Reservation.pid)

Possible Answers

Selected	Possible Answer
	1, 0
	1, 2
	1, 3
	1 , 5

Question

Which of the following concurrency control protocols ensure both conflict serializability and freedom from deadlock?
I. 2-phase locking
II. Time-stamp ordering

Possible Answers

Selected	Possible Answer
	I only
	II only
	Both I and II
	Neither I nor II

Question

The cyclomatic complexity of each of the modules A and B shown below is 10. What is the cyclomatic complexity of the sequential integration shown on the right hand side?

Possible Answers

Selected	Possible Answer
	19
	21
	20
	10

Question

What is the appropriate pairing of items in the two columns listing various activities encountered in a software life cycle?

P. Requirements Capture	1. Module Development and Integration
Q. Design	2. Domain Analysis
R. Implementation	3. Structural and Behavioral Modeling
S. Maintenance	4. Performance Tuning

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Selected	Possible Answer
	P-3, Q-2,R-4,S-1
	P-2, Q-3,R-1,S-4
	P-3, Q-2,R-1,S-4
	P-2, Q-3,R-4,S-1

Question

Consider the methods used by processes P1 and P2 for accessing their critical sections whenever needed, as given below. The initial values of shared boolean variables S1 and S2 are randomly assigned.

Which one of the following statements describes the properties achieved?

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Selected	Possible Answer
	Mutual exclusion but not progress
	Progress but not mutual exclusion
	Neither mutual exclusion nor progress
	Both mutual exclusion and progress

Question

A system uses FIFO policy for page replacement. It has 4 page frames with no pages loaded to begin with. The system first accesses 100 distinct pages in some order and then accesses the same 100 pages but now in the reverse order. How many page faults will occur?

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Selected	Possible Answer
	196
	192
	197
	195

Question

Which of the following statements are true?
I. Shortest remaining time first scheduling may cause starvation
II. Preemptive scheduling may cause starvation
III. Round robin is better than FCFS in terms of response time

Possible Answers

Selected	Possible Answer
	I only
	I and III only
	II and III only
	I, II and III

Question

Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

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Selected	Possible Answer
	pq + (1 – p) (1 – q)
	(1 – q)p
	(1 – p) q
	pq

Question

What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$ ?

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Selected	Possible Answer
	1/625
	4/625
	12/625
	16/625

Question

The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
I. 7, 6, 5, 4, 4, 3, 2, 1
II. 6, 6, 6, 6, 3, 3, 2, 2
III. 7, 6, 6, 4, 4, 3, 2, 2
IV. 8, 7, 7, 6, 4, 2, 1, 1

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Selected	Possible Answer
	I and II
	III and IV
	IV only
	II and IV

Question

Consider the following matrix
$A = \bigg[ \overset{2}{x}$ $\overset{3}{y} \bigg]$
If the eigenvalues of A are 4 and 8, then

Possible Answers

Selected	Possible Answer
	x = 4,y = 10
	x = 5,y = 8
	x = – 3,y = 9
	x = – 4,y = 10

Question

Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula $\forall x \exists y \exists t$ $( \neg F\ (x,\ y,\ t))$ ?

Possible Answers

Selected	Possible Answer
	Everyone can fool some person at some time
	No one can fool everyone all the time
	Everyone cannot fool some person all the time
	No one can fool some person at some time

Question

What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?

Possible Answers

Selected	Possible Answer
	$\overline{Q + R}$
	$\overline{P + Q}$
	$\overline{P + R}$
	$\overline{P + Q + R}$

Question

In the sequential circuit shown below, if the initial value of the output Q_1Q_0 is 00, what are the next four values of Q_1Q_0 ?

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Selected	Possible Answer
	11,10,01,00
	10,11,01,00
	10,00,01,11
	11,10,00,01

Question

A 5-stage pipelined processor has Instruction Fetch (IF), Instruction Decode (ID), Operand Fetch (OF), Perform Operation (PO) and Write Operand (WO) stages. The IF, ID, OF and WO stages take 1 clock cycle each for any instruction. The PO stage takes 1 clock cycle for ADD and SUB instructions, 3 clock cycles for MUL instruction, and 6 clock cycles for DIV instruction respectively. Operand forwarding is used in the pipeline. What is the number of clock cycles needed to execute the following sequence of instructions?

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Selected	Possible Answer
	13
	15
	17
	19

Question

The weight of a sequence $a_0, a_1 ,..., an_{-1}$ of real numbers is defined as $a_0 + a_1 /2 + ... + a_{n-1} /2^{n-1}$ . A subsequence of a sequence is obtained by deleting some elements from the sequence, keeping the order of the remaining elements the same. Let X denote the maximum possible weight of a subsequence of $a_0 ,a_1 ,..., a_{n-1}$ . Then X is equal to

Possible Answers

Selected	Possible Answer
	$max\ (Y , a_0 + Y)$

	$max\ (Y , a_0 + 2Y)$

	$None\ of\ the\ Above$

Question

What is the value printed by the following C program?
#include < stdio.h >
int f(int * a, int n)
{
if (n < = 0)return 0;
else if(*a% 2 = = 0) return * a + f(a + 1, n – 1);
else return * a – f(a + 1, n – 1);
}
int main ( )
{
int a[ ] = {12, 7, 13, 4, 11, 6};
pr int f (“%d”, f(a,6));
return 0;
}

Possible Answers

Selected	Possible Answer
	- 9
	5
	15
	19

Question

The following C function takes a simply-linked list as input argument. It modifies the list by moving the last element to the front of the list and returns the modified list. Some part of the code is left blank.

typedef struct node {
int value;
struct node *next;
} Node;
Node *move_to_front(Node *head) {
Node *p, *q;
if ((head = = NULL: || (head->next = = NULL)) return head;
q = NULL; p = head;
while (p-> next !=NULL) {
q=P;
p=p->next;
}
_________________________
return head;
}
Choose the correct alternative to replace the blank line.

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Selected	Possible Answer
	q = NULL; p->next = head; head = p;
	q->next = NULL; head = p; p->next = head;
	head = p; p->next = q; q->next = NULL;
	q->next = NULL; p->next = head; head = p;

Question

The program below uses six temporary variables a, b, c, d, e, f.
a = 1
b = 10
c = 20
d = a + b
e = c + d
f = c + e
b = c + e
e = b + f
d = 5 + e
return d + f
Assuming that all operations take their operands from registers, what is the minimum number of registers needed to execute this program without spilling?

Possible Answers

Selected	Possible Answer
	2
	3
	4
	6

Question

The grammar S $\rightarrow$ aSa|bS|c is

Possible Answers

Selected	Possible Answer
	LL(1) but not LR(1)
	LR(1) but not LR(1)
	Both LL(1) and LR(1)
	Neither LL(1) nor LR(1)

Question

Let L = {w $\in$ (0 + 1)*|w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expressions below represents L?

Possible Answers

Selected	Possible Answer
	(0 10 1) *
	0 * (10 10 ) *
	0 * (10 1) * 0 *
	0 1(10 1) 10

Question

Consider the languages $L1 = \left \{0^i 1^j\ |\ i \ne j \right \}$ . $L2 = \left \{0^i 1^j\ |\ i = j \right \}$ . $L3= \left \{0^i 1^j\ |\ i = 2j+1\right \}$ . $L4 = \left \{0^i 1^j\ |\ i \ne 2j \right \}$ . Which one of the following statements is true?

Possible Answers

Selected	Possible Answer
	Only L2 is context free
	Only L2 and L3 are context free
	Only L1 and L2 are context free
	All are context free

Question

Let w be any string of length n in {0, 1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?

Possible Answers

Selected	Possible Answer
	n-1
	n
	n+1
	$2^{n-1}$

Question

Consider the following schedule for transactions T1, T2 and T3:
T1 T2 T3
Re ad (X)
Re ad (Y)
Re ad (Y)
Write (Y)
Write (X)
Write (X)
Re ad (X)
Write (X)
Which one of the schedules below is the correct serialization of the above?

Possible Answers

Selected	Possible Answer
	$T1 \rightarrow T3 \rightarrow T2$
	$T2 \rightarrow T1 \rightarrow T3$
	$T2 \rightarrow T3 \rightarrow T1$
	$T3 \rightarrow T1 \rightarrow T2$

Question

The following functional dependencies hold for relations R(A, B, C) and S(B, D, E)
$B \rightarrow A,$
$A \rightarrow C$
The relation R contains 200tuples and the relation S contains 100tuples. What is the maximum number of tuples possible in the natural join $R \bowtie S$ ?

Possible Answers

Selected	Possible Answer
	100
	200
	300
	2000

Question

The following program is to be tested for statement coverage:
begin
if (a == b) {S1; exit;}
else if (c = = d) {S2;}
else {S3; exit;}
S4;
end
The test cases T1, T2, T3 and T4 given below are expressed in terms of the properties satisfied by the values of variables a, b, c and d. The exact values are not given.
T1 : a, b, c and d are all equal
T2 : a, b, c and d are all distinct
T3 : a=b and c !=d
T4 : a !=b and c=d
Which of the test suites given below ensures coverage of statements S1, S2, S3 and S4?

Possible Answers

Selected	Possible Answer
	T1, T2, T3
	T2, T4
	T3, T4
	T1, T2, T4

Question

The following program consists of 3 concurrent processes and 3 binary semaphores. The semaphores are initialized as S0=1, S1=0, S2=0.

How many times will process P0 print ‘0’?

Possible Answers

Selected	Possible Answer
	At least twice
	Exactly twice
	Exactly thrice
	Exactly once

Question

A system has n resources $R_0 ,..., R_{n-1},$ and k processes $P_0 ,..... P_{k-1}$ . The implementation of the resource request logic of each process Pi. is as follows:

In which one of the following situations is a deadlock possible?

Possible Answers

Selected	Possible Answer
	n = 40,k = 26
	n = 21,k = 12
	n = 20,k = 10
	n = 41,k = 19

Question

Suppose computers A and B have IP addresses 10.105.1.113 and 10.105.1.91 respectively and they both use the same net mask N. Which of the values of N given below should not be used if A and B should belong to the same network?

Possible Answers

Selected	Possible Answer
	255.255.255.0
	255.255.255.128
	255.255.255.192
	255.255.255.224

Question

Directions for next two common data questions:
A computer system has an L1 cache, an L2 cache, and a main memory unit connected as shown below. The block size in L1 cache is 4 words. The block size in L2 cache is 16 words. The memory access times are 2 nanoseconds. 20 nanoseconds and 200 nanoseconds for L1 cache, L2 cache and main memory unit respectively.

When there is a miss in L1 cache and a hit in L2 cache, a block is transferred from L2 cache to L1 cache. What is the time taken for this transfer?

Possible Answers

Selected	Possible Answer
	2 nanoseconds
	20 nanoseconds
	22 nanoseconds
	88 nanoseconds

Question

When there is a miss in both L1 cache and L2 cache, first a block is transferred from main memory to L2 cache, and then a block is transferred from L2 cache to L1 cache. What is the total time taken for these transfers?

Possible Answers

Selected	Possible Answer
	222 nanoseconds
	888 nanoseconds
	902 nanoseconds
	968 nanoseconds

Question

Directions for next two common data questions:
Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry Wij in the matrix W below is the weight of the edge {i, j}.

What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?

Possible Answers

Selected	Possible Answer
	7
	8
	9
	10

Question

What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?

Possible Answers

Selected	Possible Answer
	7
	8
	9
	10

Question

Directions for next two questions statement for linked answer questions:
A hash table of length 10 uses open addressing with hash function h(k)=k mod 10, and linear probing. After inserting 6 values into an empty hash table, the table is as shown below

Which one of the following choices gives a possible order in which the key values could have been inserted in the table?

Possible Answers

Selected	Possible Answer
	46, 42, 34, 52, 23, 33
	34, 42, 23, 52, 33, 46
	46, 34, 42, 23, 52, 33
	42, 46, 33, 23, 34, 52

Question

How many different insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above?

Possible Answers

Selected	Possible Answer
	10
	20
	30
	40

Question

Directions for next two questions statement for linked answer questions:
Consider a network with 6 routers R1 to R6 connected with links having weights as shown in the following diagram

All the routers use the distance vector based routing algorithm to update their routing tables. Each router starts with its routing table initialized to contain an entry for each neighbour with the weight of the respective connecting link. After all the routing tables stabilize, how many links in the network will never be used for carrying any data?

Possible Answers

Selected	Possible Answer
	4
	3
	2
	1

Question

Suppose the weights of all unused links in the previous question are changed to 2 and the distance vector algorithm is used again until all routing tables stabilize. How many links will now remain unused?

Possible Answers

Selected	Possible Answer
	0
	1
	2
	3

Question

Choose the most appropriate word from the options given below to the complete the following sentence:
His rather casual remarks on politics ______ his lack of seriousness about the subject.

Possible Answers

Selected	Possible Answer
	masked
	belied
	betrayed
	suppressed

Question

Which of the following options is closest in meaning to the word Circuitous.

Possible Answers

Selected	Possible Answer
	cyclic
	indirect
	confusing
	crooked

Question

Choose the most appropriate word from the options given below to complete the following sentence:
If we manage to _______ our natural resources, we would leave a better planet for our children.

Possible Answers

Selected	Possible Answer
	uphold
	restrain
	cherish
	conserve

Question

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

Possible Answers

Selected	Possible Answer
	2
	17
	13
	3

Question

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.
Unemployed: Worker

Possible Answers

Selected	Possible Answer
	fallow: land
	unaware: sleeper
	wit: jester
	renovated:house

Question

If 137+276=435 how much is 731+672?

Possible Answers

Selected	Possible Answer
	534
	1403
	1623
	1513

Question

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on $1^{st}$ january. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:
i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age
ii. The age difference between Gita and Saira is 1 year. However Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.
In what order were they born (oldest first)?

Possible Answers

Selected	Possible Answer
	HSIG
	SGHI
	IGSH
	IHSG

Question

5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Possible Answers

Selected	Possible Answer
	20
	18
	16
	15

Question

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.
Which of the following statements best sums up the meaning of the above passage:

Possible Answers

Selected	Possible Answer
	Modern warfare has resulted in civil strife.
	Chemical agents are useful in modern warfare.
	Use of chemical agents in warfare would be undesirable
	People in military establishments like to use chemical agents in war.

Question

Given digits 2,2,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000 can be formed?

Possible Answers

Selected	Possible Answer
	50
	51
	52
	54

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