Question 1

Let G=(V, E) be a graph. Define ∈(G) = ∑d id × d , where id is the number of vertices of degree d in G. If S and T are two different trees with ∈(S) = ∈(T) , then

A : |S| = 2 |T|
B : |S| = |T| -1
C : |S| = |T|
D : |S| = |T| + 1

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•   Question 2

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

A : 3.575
B : 3.676
C : 3.667
D : 3.607

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Solution :
According to Newton Raphson's method
f(x) = x2-13
f`(x) = 2x
applying formula
x1 = 3.5 - (3.5*3.5 - 13)/2*3.5
x = 3.607

•   Question 3

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

A : 210
B : 215
C : 220
D : 225

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Solution :
No. of reflexive relations is 2n2-n
substituting n=5 we get 220

•   Question 4

Consider the set S = {1, ω , ω2}, where ω and ω2 are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms

A : A group
B : A ring
C : An integral domain
D : A field

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•   Question 5

What is the value of Limn->∞(1-1/n)2n ?

A : 0
B : e-2
C : e-1/2
D : 1

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•   Question 6

The minterm expansion of f(P, Q, R) = PQ + QR' + PR' is

A : m2 + m4 + m6 + m7
B : m0 + m1 + m3 + m5
C : m0 + m1 + m6 + m7
D : m2 + m3 + m4 + m5

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•   Question 7

A main memory unit with a capacity of 4 megabytes is built using 1M x 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

A : 100*210 nanoseconds
B : 100*220 nanoseconds
C : 3200*220 nanoseconds
D : 100 nanoseconds

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Solution :
Size of main chip = 4MB
Size of a DRAM chip = 1M*(1/8)B
Number of chips needed = 32
Time for refreshing one chip = 100ns * 220

•   Question 8

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

A : (C3D8)16
B : (187B)16
C : (F878)16
D : (987B)16

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Solution :
P is 1111 1000 0111 1011 in binary
most significant bit is 1 so the number is negative.
To get the value of the number perform the 2s complement of the number.
We get P as -1925 and 8P as -15400
Since 8P is also negative, we need to find 2s complement of it (-15400) Binary of 15400

•   Question 9

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

A : ( P ⊕ Q ⊕ R )'
B : P ⊕ Q ⊕ R
C : (P+Q+R)'
D : P+Q+R

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•   Question 10

What does the following program print?
#include
void f(int *p, int *q)
{
p = q;
*p = 2;
}
int i = 0, j = 1;
int main()
{
f(&i, &j);
printf("%d %d \n", i, j);
return 0;
}

A : 2 2
B : 2 1
C : 0 1
D : 0 2

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•   Question 11

Two alternative packages A and B are available for processing a database having 10k 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?

A : 12
B : 10
C : 6
D : 5

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•   Question 12

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?

A : 0
B : 1
C : (n-1)/2
D : n-1

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Solution :
if a node has 1 child then it will be having even number of descendents which according to the question is not possible.

•   Question 13

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

A : Abstract syntax tree
B : Symbol table
C : Semantic stack
D : Parse table

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Solution :
In computer science, a symbol table is a data structure used by a language translator such as a compiler or interpreter, where each identifier in a program's source code is associated with information relating to its declaration or appearance in the source.

•   Question 14

Which languages necessarily need heap allocation in the runtime environment?

A : Those that support recursion
B : Those that use dynamic scoping
C : Those that allow dynamic data structures
D : Those that use global variables

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•   Question 15

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?

A : It can be used to prioritize packets
B : It can be used to reduce delays
C : It can be used to optimize throughput
D : It can be used to prevent packet looping

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•   Question 16

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

A : Internet chat
B : Web browsing
C : E-mail
D : ping

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Solution :
Ping is a computer network administration software utility used to test the reachability of a host on an Internet Protocol (IP) network. It measures the round-trip time for messages sent from the originating host to a destination computer that are echoed back to the source. It does not need any server for this.

•   Question 17

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?
(A) L2 - L1 is recursively enumerable.
(B) L1 – L3 is recursively enumerable
(C) L2 ∩ L1 is recursively enumerable
(D) L2 ∪ L1 is recursively enumerable

A : A
B : B
C : C
D : D

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•   Question 18

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?

A : 1
B : 2
C : 3
D : 4

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Solution :
2d-1 = 5
2d = 6
d = 3
d-1=2

•   Question 19

A relational schema for a train reservation database is given below.
What pids are returned by the following SQL query for the BELOW instance of the tables?
SELECT pid
FROM Reservation ,
WHERE class ‘AC’ AND
EXISTS (SELECT *
FROM Passenger
WHERE age > 65 AND
Passenger. pid = Reservation.pid)

A : 1,0
B : 1,2
C : 1,3
D : 1,5

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•   Question 20

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

A : I only
B : II only
C : Both I and II
D : Neither I and II

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Solution :
2 Phase Locking (2PL) is a concurrency control method that guarantees serializability. The protocol utilizes locks, applied by a transaction to data, which may block (interpreted as signals to stop) other transactions from accessing the same data during the transaction’s life. 2PL may be lead to deadlocks that result from the mutual blocking of two or more transactions.
Timestamp-based concurrency control algorithm is a non-lock concurrency control method. In Timestamp based method, deadlock cannot occur as no transaction ever waits.

•   Question 21

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?

A : 19
B : 21
C : 20
D : 10

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Solution :
CC = Number of decision points + 1
So in A and B there are 9 Decision points and in the third figure there are 18 such points so CC=18+1

•   Question 22

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

A : P-3, Q-2,R-4,S-1
B : P-2, Q-3,R-1,S-4
C : P-3, Q-2,R-1,S-4
D : P-2, Q-3,R-4,S-1

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•   Question 23

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
while (S1 == S2) ;
Critical Section
S1 = S2;

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

A : Mutual exclusion but not progress
B : Progress but not mutual exclusion
C : Neither mutual exclusion nor progress
D : Both mutual exclusion and progress

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•   Question 24

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?

A : 196
B : 195
C : 192
D : 197

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Solution :
100 Page faults then we are left with 97,98,99,100 in memory.
These 4 will not have PF rest 96 will again have page faults so total 196

•   Question 25

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

A : I only
B : I and III only
C : II and III only
D : I, II and III

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•   Question 26

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?

A : pq + (1 - p)(1 - q)
B : (1-p)p
C : (1-p)q
D : pq

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•   Question 27

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

A : 1/625
B : 4/625
C : 12/625
D : 16/625

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Solution :
Divisors are of the form :
2k * 5m
So for 1099 we have (1,21,22......299)*(1,51,52......599) divisors (one from both sets)
So there are total (100)*(100) = 10000 possibilities

•   Question 28

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

A : I and II
B : III and IV
C : IV only
D : II and IV

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•   Question 29

Consider the following matrix
If the eigenvalues of A are 4 and 8, then

A : x=4, y=10
B : x=5, y=8
C : x=3, y=9
D : x=-4, y=10

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•   Question 30

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))?

A : Everyone can fool some person at some time
B : No one can fool everyone all the time
C : Everyone cannot fool some person all the time
D : No one can fool some person at some time

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•   Question 31

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

A : (Q+R)`
B : (P+Q)`
C : (P+R)
D : (P+Q+R)`

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•   Question 32

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

A : 11, 10, 01, 00
B : 10, 11, 01, 00
C : 10, 00, 01, 11
D : 11, 10, 00, 01

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•   Question 33

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

A : 13
B : 15
C : 17
D : 19

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•   Question 34

The weight of a sequence a0, a1, ..., an-1 of real numbers is defined as a0+a1/2+...+ aa-1/2n-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, ...,an-1 and Y the maximum possible weight of a subsequence of a1, a2, ...,an-1. Then X is equal to

A : max(Y, a0+Y)
B : max(Y, a0+Y/2)
C : max(Y, a0+2Y)
D : a0+Y/2

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Solution :

The concepts involves the Dynamic Programming in Algorithms.
Given:-

X= max weight from the sequence (a0,a1,a2,....an-1) = a0+a1/2+a2/4+....+an-1/2^(n-1)
Y= max weight from the sequence (a1,a2,....an-1) = a1 + a2/2+a3/4+...+ an-1/2^(n-2)
Here we have to find X in terms of Y.

So X = [a1+a2/2+a3/4+...+ an-1/2^(n-2)] = Y
if [a0+a1/2+a2/4+....+an-1/2^(n-1)]<[a1 + a2/2+a3/4+...+ an-1/2^(n-2)]
OR

X = [a0+a1/2+a2/4+....+an-1/2^(n-1)]

•   Question 35

#include
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};
printf("%d", f(a, 6));
getchar();
return 0;
}

A : -9
B : 5
C : 15
D : 19

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•   Question 36

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 *p, *q;
q = NULL; p = head;
while (p-> next !=NULL)
{
q = p;
p = p->next;
}
_______________________________
}

```

C : head = p; p->next = q; q->next = NULL;

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•   Question 37

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?

A : 2
B : 3
C : 4
D : 6

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•   Question 38

The grammar S -> aSa | bS | c is

A : LL(1) but not LR(1)
B : LR(1)but not LR(1)
C : Both LL(1)and LR(1)
D : Neither LL(1)nor LR(1)

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•   Question 39

Let L={w ∈ (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 expression below represents L?

A : (0*10*1)*
B : 0*(10*10*)*
C : 0*(10*1*)*0*
D : 0*1(10*1)*10*

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•   Question 40

Consider the languages
L1 = {0i1j | i ≠ j}.
L2 = {0i1j | i = j}.
L3 = {0i1j | i = 2j+1}.
L4 = {0i1j | i != 2j}.

A : Only L2 is context free
B : Only L2 and L3 are context free
C : Only L1 and L2 are context free
D : All are context free

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•   Question 41

Let w be any string of length n is {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?

A : n-1
B : n
C : n+1
D : 2n-1

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Solution :
all the n states in the max length substring that is the string itself and one final state so n+1

•   Question 42

Consider the following schedule for transactions T1, T2 and T3.Which one of the schedules below is the correct serialization of the above?

A : T1 -> T3 -> T2
B : T2 -> T1 -> T3
C : T2 -> T3 -> T1
D : T3 -> T1 -> T2

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•   Question 43

Which of the following functional dependencies hold for relations R(A, B, C) and S(B, D, E):
B -> A
A -> C
The relation R contains 200 tuples and the rel ation S contains 100 tuples. What is the maximum number of tuples possible in the natural join of R and S (R natural join S)

A : 100
B : 200
C : 300
D : 2000

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Solution :
From the given set of functional dependencies, it can be observed that B is a candidate key of R. So all 200 values of B must be unique in R. There is no functional dependency given for S. To get the maximum number of tuples in output, there can be two possibilities for S.

1) All 100 values of B in S are same and there is an entry in R that matches with this value. In this case, we get 100 tuples in output.

2) All 100 values of B in S are different and these values are present in R also. In this case also, we get 100 tuples.

•   Question 44

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 given below ensures coverage of statements S1, S2, S3 and S4?

A : T1, T2, T3
B : T2, T4
C : T3, T4
D : T1, T2, T4

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•   Question 45

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’?

A : At least twice
B : Exactly twice
C : Exactly thrice
D : Exactly once

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•   Question 46

A system has n resources R0,...,Rn-1,and k processes P0,....Pk-1.The implementation of the resource request logic of each process Pi 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 one of the following situations is a deadlock possible?

A : n=40, k=26
B : n=21, k=12
C : n=20, k=10
D : n=41, k=19

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•   Question 47

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

A : 255.255.255.0
B : 255.255.255.128
C : 255.255.255.192
D : 255.255.255.224

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Solution :
The first 3 blocks are the same and the Forth block has 113= 1110001 and 91=1101111. Only 2 bits should be same as in first 3 options

•   Question 48

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?

A : 2 nanoseconds
B : 20 nanoseconds
C : 22 nanoseconds
D : 88 nanoseconds

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Solution :
16/4 = 4 so we have to copy the block 4 times and place it in the L1 cache. So (20+2)*4 = 88

•   Question 49

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?

A : 222 nanoseconds
B : 888 nanoseconds
C : 902 nanoseconds
D : 968 nanoseconds

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Solution :
Time between memory and L2 cache = 200+20
Time between L2 and L1 is 20+2
now total there is a transfer of 4 words between each unit so 4*(220+22)

•   Question 50

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?

A : 7
B : 8
C : 9
D : 10

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•   Question 51

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 path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?

A : 7
B : 8
C : 9
D : 10

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•   Question 52

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?

A : 46, 42, 34, 52, 23, 33
B : 34, 42, 23, 52, 33, 46
C : 46, 34, 42, 23, 52, 33
D : 42, 46, 33, 23, 34, 52

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•   Question 53

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?
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?

A : 10
B : 20
C : 30
D : 40

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•   Question 54

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?

A : 4
B : 3
C : 2
D : 1

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•   Question 55

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?

A : 0
B : 1
C : 2
D : 3

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•   Question 56

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.

B : belied
C : betrayed
D : suppressed

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•   Question 57

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

A : cyclic
B : indirect
C : confusing
D : crooked

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•   Question 58

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.

A : uphold
B : restrain
C : cherish
D : conserve

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•   Question 59

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:

A : 2
B : 17
C : 13
D : 3

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•   Question 60

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

A : fallow: land
B : unaware: sleeper
C : wit: jester
D : renovated: house

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•   Question 61

Hari(H), Gita(G), Irfan(I) and Saira(S) are siblings (i.e., brothers and sisters). All were born on 1st 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 bor

A : HSIG
B : SGHI
C : IGSH
D : IHSG

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•   Question 62

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:

A : Modern warfare has resulted in civil strife.
B : Chemical agents are useful in modern warfare.
C : Use of chemical agents in warfare would be undesir
D : People in military establishments like to use chem

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•   Question 63

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

A : 534
B : 1403
C : 1623
D : 1513

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•   Question 64

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

A : 20
B : 10
C : 16
D : 15

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•   Question 65

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

A : 50
B : 51
C : 52
D : 54

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