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. |Method used by P1| Method used by P2| |----|----| |while (S1==S2); | while (S1!=S2); | |Critical Section | Critical Section | |S1=S2; | S2 = not(S1) | Which one of the following statements describes the properties achieved?

Mutual exclusion but not progress

Computer Science (GATE Exam) 2010 - Previous Question Paper Solution

Question 1 Multiple Choice (Single Answer)

Let G=(V, E) be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, 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

$\mid$S$\mid$ = 2$\mid$T$\mid$
$\mid$S$\mid$ = $\mid$T$\mid$ - 1
$\mid$S$\mid$ = $\mid$T$\mid$
$\mid$S$\mid$ = $\mid$T$\mid$ + 1

Question 2 Multiple Choice (Single Answer)

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

a group
a ring
an integral domain
a field

Question 3 Multiple Choice (Single Answer)

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?

0
1
(n − 1) / 2
n -1

Question 4 Multiple Choice (Single Answer)

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

(C3D8)₁₆
(187B)₁₆
(F878)₁₆
(987B)₁₆

Question 5 Multiple Choice (Single Answer)

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

Abstract syntax tree
Symbol table
Semantic stack
Parse table

Question 6 Multiple Choice (Single Answer)

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

100 nanoseconds
100*2¹⁰ nanoseconds
100*2²⁰ nanoseconds
3200*2²⁰ nanoseconds

Question 7 Multiple Choice (Single Answer)

Two alternative packages A and B are available for processing a database having 10^k records. Package A requires 0.0001n² time units and package B requires 10nlog₁₀n time units to process n records. What is the smallest value of k for which package B will be preferred over A?

12
10
6
5

Question 8 Multiple Choice (Single Answer)

Which languages necessarily need heap allocation in the runtime environment?

Those that support recursion.
Those that use dynamic scoping.
Those that allow dynamic data structures.
Those that use global variables.

Question 9 Multiple Choice (Single Answer)

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?

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 10 Multiple Choice (Single Answer)

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

Internet chat
Web browsing
E-mail
Ping

Question 11 Multiple Choice (Single Answer)

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?

1
2
3
4

Question 12 Multiple Choice (Single Answer)

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);
print f ("%d%d  n", i, j) ;
return 0;
}
```</stdio.h>

2 2
2 1
0 1
0 2

Question 13 Multiple Choice (Single Answer)

Newton-Raphson method is used to compute a root of the equation x² − 13 = 0 with 3.5 as the initial value. The approximation after one iteration is

3.575
3.676
3.667
3.393

Question 14 Multiple Choice (Single Answer)

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

Only I
Only II
Both I and II
Neither I nor II

Question 15 Multiple Choice (Single Answer)

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?

L2 - L1 is recursively enumerable
L1 - L3 is recursively enumerable
L2 $\cap$ L1 is recursively enumerable
L2 $\cup$ L1 is recursively enumerable

Question 16 Multiple Choice (Single Answer)

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?

19
21
20
10

Question 17 Multiple Choice (Single Answer)

What is the value of $\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?

0
e^-2
e^-1/2
1

Question 18 Multiple Choice (Single Answer)

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?

196
192
197
195

Question 19 Multiple Choice (Single Answer)

A relational schema for a train reservation database is given below:
Passenger (pid, pname, age)

Table: passenger

pid	pname	Age
0	Sachin	65
1	Rahul	66
2	Sourav	67
3	Anil	69

Table: Reservation

pid	class	tid
0	AC	8200
1	AC	8201
2	SC	8201
5	AC	8203
1	SC	8204
3	AC	8202

What pids are returned by the following SQL query for the above instance of the tables?

SELECT           pid
FROM  Reservation
WHERE           class 'AC' AND
                        EXISTS (SELECT *
                        FROM Passenger
                        WHERE age 65 > AND
                        Passenger. pid = Reservation. pid)

1, 0
1, 2
1, 3
1, 5

Question 20 Multiple Choice (Single Answer)

What is the probability that divisor of 1099 is a multiple of 1096?

1/625
4/625
12/625
16/625

Question 21 Multiple Choice (Single Answer)

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

I only
I and III only
II and III only
I, II and III

Question 22 Multiple Choice (Single Answer)

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?

pq + (1 − p) (1 − q)
(1 − q)p
(1 − p) q
pq

Question 23 Multiple Choice (Single Answer)

Consider the following matrix $$A = \left[\begin{array}{cc}2 & 3\\ x & y \end{array}\right]$$ If the eigenvalues of A are 4 and 8, then

x = 4, y = 10
x = 5, y = 8
x = −3, y = 9
x = −4, y = 10

Question 24 Multiple Choice (Single Answer)

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.

Method used by P1	Method used by P2
while (S1==S2);	while (S1!=S2);
Critical Section	Critical Section
S1=S2;	S2 = not(S1)

Which one of the following statements describes the properties achieved?

Mutual exclusion but not progress
Progress but not mutual exclusion
Neither mutual exclusion nor progress
Both mutual exclusion and progress

Question 25 Multiple Choice (Single Answer)

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

I and II
III and IV
IV only
II and IV

Question 26 Multiple Choice (Single Answer)

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

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 27 Multiple Choice (Single Answer)

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

2¹⁰
2¹⁵
2²⁰
2²⁵

Question 28 Multiple Choice (Single Answer)

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 $∀x∃y∃t(¬F(x,y,t))$?

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 29 Multiple Choice (Single Answer)

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
  };
  print f( % d, f(a, 6));
  return 0;
}

-9
5
15
19

Question 30 Multiple Choice (Single Answer)

In the sequential circuit shown below, if the initial value of the output Q₁Q₀ is 00, what are the next four values of Q₁Q₀?

11,10,01,00
10,11,01,00
10,00,01,11
11,10,00,01

Question 31 Multiple Choice (Single Answer)

The weight of a sequence a₀, a₁,…, a_n-1 of real numbers is defined as a + a₁ / 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 a₀, a₁, …., a_n-1. Then X is equal to

max (Y, a₀ + Y)
max (Y, a₀ + Y/2)
max (Y, a₀ +2Y)
a₀ + Y / 2

Question 32 Multiple Choice (Single Answer)

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

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 33 Multiple Choice (Single Answer)

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.

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 34 Multiple Choice (Single Answer)

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?

255.255.255.0
255.255.255.128
255.255.255.192
255.255.255.224

Question 35 Multiple Choice (Single Answer)

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?

Instruction Meaning of instruction
$t_0: MUL :R_2,R_0,R_1$ $R_2 \gets R_0*R_1$
$t_1: DIV: R_5,R_3,R_4$ $R_5 \gets R_3 / R_4$
$t_2: ADD: R_2,R_5,R_2$ $R_2 \gets R_5 + R_2$
$t_3: SUB :R_5,R_2,R_6$ $R_5 \gets R_2 - R_6$

13
15
17
19

Question 36 Multiple Choice (Single Answer)

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}.
W =

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?

7
8
9
10

Question 37 Multiple Choice (Single Answer)

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?

4
3
2
1

Question 38 Multiple Choice (Single Answer)

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

if (i%2==0) { 
    if (i<n) request Ri; 
    if (i+2 < n) request Ri+2 
}

else { 
    if (i<n) request Rn-i; 
    if (i+2 <n) request Rn-i-2; 
}

In which of the following situations is a deadlock possible?

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

Question 39 Multiple Choice (Single Answer)

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?

2
3
4
6

Question 40 Multiple Choice (Single Answer)

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?

2 nanoseconds
20 nanoseconds
22 nanoseconds
88 nanoseconds

Question 41 Multiple Choice (Single Answer)

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

0
1
2	42
3	23
4	34
5	52
6	46
7	33
8
9

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?

10
20
30
40

Question 42 Multiple Choice (Single Answer)

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 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?

222 nanoseconds
888 nanoseconds
902 nanoseconds
968 nanoseconds

Question 43 Multiple Choice (Single Answer)

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


Process P0	Process P1	Process P2
while (true) {	wait (S1);	wait (S2);
wait (S0);	release (S0);	release (S0);
print '0';
release (S1);
release (S2);
}

How many times will process P0 print ‘0’?

At least twice
Exactly twice
Exactly thrice
Exactly once

Question 44 Multiple Choice (Single Answer)

Directions: 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.

masked
belied
betrayed
suppressed

Question 45 Multiple Choice (Single Answer)

Consider a network with 6 routers R1 to R6 connected with links having weights as shown in the following diagram

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?

0
1
2
3

Question 46 Multiple Choice (Single Answer)

Directions: 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.

uphold
restrain
cherish
conserve

Question 47 Multiple Choice (Single Answer)

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

fallow : land
unaware : sleeper
wit : jester
renovated : house

Question 48 Multiple Choice (Single Answer)

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?

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 49 Multiple Choice (Single Answer)

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

534
1403
1623
1513

Question 50 Multiple Choice (Single Answer)

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

cyclic
indirect
confusing
crooked

Question 51 Multiple Choice (Single Answer)

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

0
1
2	42
3	23
4	34
5	52
6	46
7	33
8
9

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

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 52 Multiple Choice (Single Answer)

Consider the following schedule for transactions T1, T2 and T3:

$\underline {T1}$	$\underline{T2}$	$\underline{T1}$
Read(X)
	Read(Y)
		Read(Y)
	Write(Y)
Write(X)
		Write(X)
	Read(X)
	Write(X)

Which one of the schedules below is the correct serialization of the above?

T1 $\rightarrow$ T3 $\rightarrow$ T2
T2 $\rightarrow$ T1 $\rightarrow$ T3
T2 $\rightarrow$ T3 $\rightarrow$ T1
T3 $\rightarrow$ T1 $\rightarrow$ T2

Question 53 Multiple Choice (Single Answer)

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?

20
18
16
15

Question 54 Multiple Choice (Single Answer)

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?

n - 1
n
n + 1
2^n-1

Question 55 Multiple Choice (Single Answer)

Consider the languages L1 = {0ⁱ1^j | i $\ne$ j}. L2 = {0ⁱ1^j | i = j}. L3 = {0ⁱ1^j | i = 2j +1}.
L4 = {0ⁱ1^j | i $\ne$2j}. Which one of the following statements is true?

Only L2 is context free
Only L2 and L3 are context free
Only L1 and L2 are context free
All are context free

Question 56 Multiple Choice (Single Answer)

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}.
W =

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?

7
8
9
10

Question 57 Multiple Choice (Single Answer)

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)?

HSIG
SGHI
IGSH
IHSG

Question 58 Multiple Choice (Single Answer)

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

50
51
52
54

Question 59 Multiple Choice (Single Answer)

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?

T1, T2, T3
T2, T4
T3, T4
T1, T2, T4

Question 60 Multiple Choice (Single Answer)

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 $R \bowtie S$

100
200
300
2000

Question 61 Multiple Choice (Single Answer)

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

2
17
13
3

Question 62 Multiple Choice (Single Answer)

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

m₂ + m₄ + m₆ + m₇
m₀ + m₁ + m₃ + m₅
m₀ + m₁ + m₆ + m₇
m₂ + m₃ + m₄ + m₅

Question 63 Multiple Choice (Single Answer)

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

$\overline{P \oplus Q \oplus R }$
${P \oplus Q \oplus R }$
P + Q + R
$\overline{P + Q + R }$

Question 64 Multiple Choice (Single Answer)

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

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

Computer Science (GATE Exam) 2010 - Previous Question Paper Solution

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