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Test series

Full Length Mock test for GATE 2021 (CS/IT)

Mock Test 1

Solutions

Question 1

You didn't Attempt

Choose the word which best expresses the meaning of given word

Dreadfully

Incredibly

Correct answer

Disastrous

Sad

none of above

Solution

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Dreadfully closest meaning is incredibly here

General Studies & AptitudeLogical Reasoning

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Question 2

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Choose the word which is antonym if given word

ENORMOUS

Soft

Average

Tiny

Correct answer

Weak

Solution

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Enormous means huge amount, Tiny means less

General Studies & AptitudeLogical Reasoning

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Question 3

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choose the word which can be best substituted

Extreme old age when a man behaves like a fool

Imbecility

Senility

Dotage

Correct answer

Superannuation

Solution

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Dotage is most appropriate word over here

General Studies & AptitudeLogical Reasoning

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Question 4

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Find the remainder when $(100!)^{(10000)}$ is divided by 23?

Correct answer

Solution

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We know that 100! = 100 * 99 * 98 * … * 23 * 22 * 21 * … * 3 * 2 * 1

So when this equation is divided by 23, the remainder is 0.

General Studies & AptitudeLogical Reasoning

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Question 5

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Aman’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. What is Aman’s speed against the current?

8.5 km/hr

9 km/hr

10 km/hr

Correct answer

12.5 km/hr

Solution

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Aman’s rate in still water = (15 – 2.5) = 12.5 km/hr. Aman’s rate

(12.5 – 2.5) km/hr = 10 km/hr.

General Studies & AptitudeLogical Reasoning

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Question 6

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Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

6:7:8

2:3:4

Correct answer

6:8:9

None of the above

Solution

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Let the ratios of division be = 5x:7x:8x

There is an increase of 40%, 50% and 75% respectively.

Therefore, applying the % over the ratio we get, 7x:21x/2:14x

So, this is the required ratio.

= 14x : 21x: 28x

= 2 : 3 : 4

General Studies & AptitudeLogical Reasoning

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Question 7

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In a circle of radius 5 cm AB and AC are length of chords of 6cm each the length of chords BC is

24/5

7/5

48/5

Correct answer

12/5

Solution

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$\begin{aligned} & { From\ the\ given\ figure, } \mathrm{AD}=(5-\mathrm{x}) \mathrm{cm}\\ &{ In\ triangle } \mathrm{ABD}, \mathrm{AB}^{2}=\mathrm{AD}^{2}+\mathrm{BD}^{2} \end{aligned}$

$\begin{aligned} & { i.e. } 6^{2}=(5-x)^{2}+s^{2}\\ &\therefore \mathrm{s}^{2}=36-(5-\mathrm{x})^{2} \quad \ldots(1) \end{aligned}$

$\begin{aligned} &{ In\ triangle } \mathrm{\ ADO}, \mathrm{BO}^{2}=\mathrm{OD}^{2}+\mathrm{BD}^{2}\\ &{ i.e. } 5^{2}=x^{2}+s^{2}\\ &\therefore \mathrm{s}^{2}=25-\mathrm{x}^{2} \ldots(2) \end{aligned}$

$From \ equation\ ( 1 ) \ and \ ( 2 )\\ 36-(5-x)^{2}=25-x^{2}$

x=7/5 putting in (2) we get 48/5

General Studies & AptitudeLogical Reasoning

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Question 8

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Rohit’s father is three times older than Rohit. After 8 years, he would be two and a half times of Rohit’s age. After a further 8 years, how many times would he be of Rohit’s age?

2 times

Correct answer

2.5 times

2.75 times

3 times.

Solution

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Let Rohit present age be x years

Therefore father’s age is x + 3x = 4x years

According to the question,

4x + 8 = 5/2(x + 8)

=> 3x = 24

=> x = 8

So the answer is: (4x + 16) / (x + 16) = 48/24 = 2

General Studies & AptitudeLogical Reasoning

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Question 9

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A ship, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream in km/hr?

Correct answer

Solution

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Let the speed of the stream be x km/hr.

Therefore the, speed of downstream = (15 + x) km/hr,

and speed of upstream = (15 – x) km/hr.

According to the question,

30/(15 + x) + 30/(15 – x) = 9/2

or, 900/(225 – $true$ ) = 9/2

or, $true$ = 225

or, $true$ = 25

or, x = 5 km/hr.

General Studies & AptitudeLogical Reasoning

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Question 10

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Insert the missing number.

8, 7, 11, 12, 14, 17, 17, 22, (......)

Correct answer

Solution

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There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22) increasing by 3 and 5 respectively.

General Studies & AptitudeLogical Reasoning

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Question 11

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Consider the cryptosystem

Above cryptosystem is___

Symmetric Key Cryptosystem

Correct answer

Public Key cryptosystem

Digital Signature

None of these

Solution

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both sender and Receiver can share the same key in symmetric key cryptography

Computer NetworkCryptography

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Question 12

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Find the number of ways of getting number of tail more than 1 time in n flips(n>3)

$true$

Correct answer

$true$

Solution

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$\mathrm{P}$ (number of tails $\leq 1$ )

$&=\mathrm{P}(\# \mathrm{T'S}=0)+\mathrm{P}\left(\# \mathrm{T}^{\prime} \mathrm{S}=1\right) \\ &=1+{ }^{\mathrm{n}} \mathrm{C}_{1} \\ &=1+\mathrm{n} \\$

$\mathrm{P}\left(\# \mathrm{T}^{\prime} \mathrm{s}>1\right)$

$&=2^{n}-\left(\# \mathrm{T}^{\prime} \mathrm{S} \leq 1\right) \\ &=2^{n}-(1+\mathrm{n}) \\ &=2^{n}-\mathrm{n}-1$

Discrete MathematicsSets

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Question 13

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Find which of the following is incorrect

ARP is used to find MAC address of the given IP address

ALOHA does not sense carrier and transmit whenever it has data

TCP guarantees error free and ordered data delivery

CSMA sense carrier and transmit whenever it has data

Correct answer

Solution

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CSMA senses data and transmits data if the medium is idle. CSMA will not transmit whenever it has data , it only transmit when the medium is idle.

Computer NetworkNetwork Layer Protocols

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Question 14

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$A=\left[\begin{array}{rrr} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & 1 \end{array}\right]$ , $true$ ______?

Idempotent

Nilpotent

Involutory

Correct answer

None of these

Solution

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$A^{2}=\left[\begin{array}{rrr} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & 1 \end{array}\right]\left[\begin{array}{rrr} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & 1 \end{array}\right]$

$=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]=I$

Discrete MathematicsFunctions

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Question 15

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Let $true$ be an antisymmetric relation and $true$ is inverse of , $true$ ie. $R_1^{-1}$ . Find the R1 U R2 ?

Symmetric Relation

Correct answer

Antisymmetric relation

Asymmetric Relation

None of the above

Solution

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Clearly if (a,b) is present in $true$ so (b,a) will be present in $R_1^{-1}$ . Hence $true$ U $true$ will be Symmetric relation

Discrete MathematicsRelations

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Question 16

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Consider the Johnson counter consisting of 5FF. If this counter has P states and it counts maximum decimal number Q, the correct values of P and Q are

P=32 Q=32

P=10 Q=31

Correct answer

P=31 Q=10

P=10 Q=32

Solution

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Johnson counter contain 2n state for nFF

So, P=10

Also with nFF the maximum count by this counter is $true$

So, Q=31

Digital LogicCounter

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Question 17

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Match the following

$true$ $true$

A. $\left\{a^{n^{2}}\right\}$ 1. DCFL

B. $\left\{a^{3 n+5} \mid n \geq 0\right\}$ 2. CFL

C. $\left\{a^{n} b^{m} c^{m} d^{n} \mid n, m \geq 0\right\}$ 3. CSL

D. $\left\{w \times w^{R} \mid w \in\{0,1\}^{*}, x \in\{0,1\}\right\}$ 4. Regular

A B C D

(a) 3 2 1 4

(b) 3 4 1 2

(d) 4 3 2 1

(a)

(b)

Correct answer

(c)

(d)

Solution

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$a^{n^{2}} \rightarrow$ non-linear power $-\mathrm{CSL}$

$a^{3 n}+5 \rightarrow($ aaa $)^{\star}$ aaaa $\rightarrow$ regular

$a^{n} b^{m} c^{m} d^{n} \rightarrow$ DCFL (push pop easily done)

$\mathrm{w} \times \mathrm{w}^{\mathrm{R}} \rightarrow \mathrm{CFL}\{$ as $\mathrm{x} \in(0,1)\}$ and $\mathrm{w} \in\{0,1\}^{\star}$

Theory of ComputationLanguage

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Question 18

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Quick sort algorithm is run on two input list shown below

List1: 1,2,3,4….

List2: n,n-1,n-2……

Let $true$ and $true$ are no of Comparison made for input $true$ and $true$ then

$true$

Correct answer

$true$

none of above

Solution

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Quicksort on already sorted Input behaves as worst case O( $true$ )

AlgorithmsDivide and Conquer

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Question 19

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Consider the homomorphism function

$h: \Sigma \rightarrow \Delta^{*},$ where $\Sigma\{0,1\}$ and $\Delta=\{a, b\}$

and $true$

if $L=\{00,01,101\}$ then $true$ will be _______

{aaaa,aabb,bbaabb}

Correct answer

{aa,ab,aba}

{aaa,bba,aabbaa}

none of the above

Solution

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By Substituting 0 as aa and 1 as bb

Theory of ComputationTheory of Computation

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Question 20

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Assume process A has 3 user level thread and process B has 4 kernel level thread. Assume while process A is running in CPU ,process B is waiting in the ready queue. If one of the thread of A gets blocked Find the status of process of A and B

All A thread get blocks and All B thread gets blocked

All A thread are not blocks and All B thread gets blocked

All A thread get blocks and All B thread are not blocked

Correct answer

none of the above

Solution

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For process A , gets a single control block instead a control block for each thread So, blocking one thread will block all the thread for user level thread

Operating SystemDeadlock

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Question 21

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Number of 0 's present in $true$ 's Complementation of $(-127)_{10} ?$

Correct answer

Solution

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Binary representation of $127_{10} \quad 01111111$

In 2's complement $-127_{10} 10000001$

There are 6 0’s are present

Digital ElectronicsNumber System

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Question 22

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Consider the following page reference string

$true$

Assume there are 4 frame and initially all are empty

Using optimal Strategy, find the number of page faults ?

Correct answer

Solution

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So, no of page faults are 8

Operating SystemVirtual Memory

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Question 23

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What will be the output of the following program?

#include<stdio.h>

void main()

{

int p=0, q=2, s,t;

s= p++ && ++q ;

printf("%d %d \n",p, s);

}

1 0

Correct answer

0 0

1 1

1 0

Solution

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Precedence of pre increment and post increment are greater than &&.

Post increment has higher precedence than pre increment.

But when a postfix increment is present in an equation, it will be incremented after the value is being assigned or used in the equation.

Hence,

p++ => here p will be considered as 0

++q => here q will be incremented to 3

And operation will take place in 0 and 3 giving to 0, hence s will be 0.

Now p will be incremented to 1.

Hence, output will be 1 0

Programming & Data StructureC Programming

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Question 24

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Which of the following codes is a self-complementary code?

8 4 -2 -1

6 3 1 -1

2421

All

Correct answer

Solution

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All the given codes are self-complementary codes.

Digital ElectronicsBoolean Algebra

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Question 25

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MInimal form of $x+z+x^{\prime} y+x^{\prime} y^{\prime} z^{\prime}$ is

Correct answer

x+z

x+y

y+z

Solution

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$x+z+x^{\prime} y+x^{\prime} y^{\prime} z^{\prime}=\left(x+x^{\prime} y\right)+\left(z+x^{\prime} y^{\prime} z^{\prime}\right)$

$=(x+y)+\left(z+x^{\prime} y^{\prime}\right)$ ( ∵ Distribution of OR over AND)

$=\left(x+x^{\prime} y^{\prime}\right)+y+z \\ =\left(x+y^{\prime}\right)+y+z\left(\because y+y^{\prime}=1\right) \\ =1$

Digital ElectronicsBoolean Algebra

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Question 26

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What is the time complexity of the following code?

void Knowledge(n)

{

int i, j, k, count = 0;

for(i = n/4; i <= n; i++)

for( j = 1; j <= n/2; j = j*2)

for(k = 1; k*k <= n; k++)

count++;

}

$\mathrm{O}\left(\mathrm{n}^{2} \log \mathrm{n}\right)$

$\mathrm{O}\left(\mathrm{n}^{3/ 2} \log \mathrm{n}\right)$

Correct answer

$O\left(n \log ^{2} n\right)$

$O\left(n^{3}\right)$

Solution

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If you see outer loop it is running for O(n)

inner loop for j-> logn times

inner loop for k-> sqrt(n)

Total time complexity -> n * $n^{1/2 }$ * logn

AlgorithmsAlgorithms

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Question 27

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Consider the following statements with respect to network security

a. Message confidentiality means that the sender and the receiver expect privacy.

b. Message integrity means that the data must arrive at the receiver exactly as they were sent.

c. Message authentication means the receiver ensured that the message is coming from the intended sender.

Which of the statements is (are)correct?

only (a) and (b)

only (a) and (c)

only (b) and (c)

(a), (b) and (c)

Correct answer

Solution

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Message Confidentiality:

It means a set of rules and promises which are executed through confidentiality agreements.

Message Integrity:

It means that the data must not be modified in the transit.

Message Authentication:

It is the property that the message is not changed and also the source can be verified by the receiver.

Computer NetworkNetwork Security

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Question 28

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The number of faces( regions ) in a complete graph of 5 vertices ___

Correct answer

Solution

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Number of edges in a complete graph of 5 vertices = n(n-1)/2 = 10

Euler's formula:

V - E + F = 2

5-10+F=2

F =7

Network TheoryGraph Theory

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Question 29

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Dijkstra’s shortest-path algorithm may relax an edge more than once in a graph with a cycle.

true

false

Correct answer

may be may not be

none of above

Solution

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Dijkstra’s algorithm always visits each node at most once; this is why it produces an incorrect result in the presence of negative-weight edges.

AlgorithmsGreedy Techniques

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Question 30

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In the IPv4 addressing format, the number of networks allowed under Class B addresses is

$2^{14}$

Correct answer

$2^{7}$

$2^{16}$

$2^{24}$

Solution

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In class B, 16 bits are reserved for Host Id and 16 bits are reserved for Network Id. Out of these 16 Network Id bits, the leading 2 bits are fixed as 10. So remaining 14 bits can be used for different networks.

Computer NetworkNetwork Layer Introduction

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Question 31

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Suppose the X has a continuous uniform distribution over the interval.[-1,1]

The mean of a random variable is

-

Your answer

0

Correct answer

Solution

Hide

Discrete MathematicsFunctions

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Question 32

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Find the number of tokens in the given code

void $\ ^*{fun}$ $true$ int $\ ^*a$ , int $\ ^*b$ );

-

Your answer

15

Correct answer

Solution

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void * $true$ ) ( int * $true$ , int * $true$ );

Tokens: void $\mid(|*|$ fun $\mid) \mid(\mid$ int $|*| \mathrm{a}|,|$ int $|*| \mathrm{b} \mid) \mid$

$true$ tokens in the given code.

Compiler DesignLexical Analysis

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Question 33

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$[2 D]_{16}$ in BCD $true$ is

-

Your answer

01000101

Correct answer

Solution

Hide

Digital ElectronicsNumber System

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Question 34

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Consider a 2048 * 8 bit, byte addressable rom,which has 2 select inputs and operates on 5V power supply. find number of pins needed for such IC package

-

Your answer

23

Correct answer

Solution

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$2048 \times 8$ -bits $\Rightarrow 2^{11} \times 8$ -bits

Address lines $true$

$Data lines =8\\ Select inputs =2\\ Power \quad=1\\ \underline {Ground =1}\\ \underline{Total \quad}=23$

COAControl Unit and Design

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Question 35

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The maximum number of articulation points in any binary tree of 50 nodes are____?

-

Your answer

48

Correct answer

Solution

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The maximum number of articulation points in any binary tree is only possible when it is skewed . hence for n nodes n-2 articulations points

Network TheoryGraph Theory

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Question 36

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Consider a byte addressable memory system with 32bits Virtual addresses, 30bits physical addresses and 4KB page size. The TLB is 4-way set associative, with 16 total entries. The cache is 2-way set associative with 8-byte blocks, and 16 total lines. Determine the physical address bits assigned to Physical Page Number (PPN), Physical Page Offset (PPO), Cache Offset (CO), Cache Index (CI) and Cache Tag (CT) in that order from the options given below :

PPN: 12, PPO: 18, CO: 3, CI: 3, CT: 12

PPN: 18, PPO: 12, CO: 6, CI: 6, CT: 12

PPN: 18, PPO: 12, CO: 8, CI: 6, CT: 12

PPN: 18, PPO: 12, CO: 3, CI: 3, CT: 12

Correct answer

Solution

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Physical Page Number (PPN) : $2^{30}$ B/4KB = $2^{30}$ / $2^{12}$ => 18 bits.

Physical Page Offset (PPO) : 30bits – 18bits = 12bits.

Cache Offset (CO) : Cache block size is 8Bytes => 3bits.

Cache Index (CI) : No.of Cache sets = 16/2 = 8 => 3bits.

Cache Tag (CT) : CT = PPN – CI -CO = 18-3-3 = 12bits.

Operating SystemMemory Management

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Question 37

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A B-tree is used as an index for a large database table has 85 nodes. Order of B tree is 4. [Assume every node is full]. If a new key is inserted in this index, then the maximum number of nodes that could be newly created in the process

Correct answer

None of the above

Solution

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Given No. of nodes in $\mathrm{B}$ tree $true$

Order of $\mathrm{B}$ tree $=4[\mathrm{Max}$ no. of child $true$ block pointers in a node $true$

Let no. of levels $true$

$\therefore 4^{0}+4^{1}+4^{2}+\ldots+4^{l-1}=85 \\ \frac{1\left(4^{\prime}-1\right)}{3}=85 \\ \left(4^{l}-1\right)=255 \\ 4^{2}=256 \\ \Rightarrow[l=4$

No. of levels $true$

$Given,\ every\ node \ is\ full.$

Then the maximum number of nodes will be created if we insert the key at leaf level.

So, no. of new nodes created =5

Database Management SystemB-Tree

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Question 38

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Consider the microprogrammed control unit which supports 128 instructions, each of which on an average takes 4 micro operations. The system supports 14 flag conditions and two groups of control signals which are a total of 55 control signals. Group-1 has to generate one or none of 50 control signals and group-2 can have at most 5 from the remaining control signals. What is the minimum size of the control word?(Note Group 2 is using Horizontal microprogrammingand Group 1 is Vertical microprogramming)

Correct answer

Solution

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Number of words in control memory = 128 * 4 = 2^9 words

Address field = 9 bits

There are 14 flags. So no. of bits for the 14(next power of 2, 2^4) flags = 4

In the control signals, group-1 it has to generate one or none of the 50 control signals..

These can be represented using encoding, ceil(log50) = 6 bits.

Group-2 can have at most 5 signals… to represent these 5 signals each can be represented with one bit. So 5 bits are needed for group-2 signals.

Total bits for the control signals = 6+5 = 11 bits

Control word contains the following 3 fields:

Control word size = 4+11+9 = 24 bits

COACISC and RISC Architectures

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Question 39

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Suppose that a message 1001 1100 1010 0011 is transmitted using Internet Checksum (4-bit word). What is the value of the checksum?

100100

101010

100010

None

Correct answer

Solution

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For 4-bit checksum, we have to divide the message into 4-bit words and add all.

1001 + 1100 + 1010 + 0011 = 100010

We want 4-bit checksum, bring 10 down and so add

0010 + 10 = 0100

And checksum will be the complement of 0100 which is 1011.

Computer NetworkTransport Layer

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Question 40

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Consider the following message:ABBABCDDCCBCCDDDA

What is the average length of bits required for encoding each letter using Huffman coding is ____?

none of the above

Correct answer

Solution

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ABBABCDDCCBCCDDDA

Arrange the letters in increasing order of the frequency of its occurrence

A=3

B=4

C=5

D=5

Total bits =2*3+2*4+2*5+2*5=34

Average length =34/17=2

AlgorithmsApplications of Greedy Techniques

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Question 41

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Which of the following is/are application of NFA/DFA

String matching

lexical analysis

text editor

all

Correct answer

Solution

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Application of NFA/DFA are

String matching,lexical analysis,text editor and spell checker

Theory of ComputationFinite Automata

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Question 42

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If a is the element of the finite group G, then for any b in G and integer k>0 $\left(a b a^{-1}\right)^{k}$ is

$\mathrm{aba}^{-1}$

$\mathrm{b}^{k}$

$a b^{2} a^{-1}$

Correct answer

Solution

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Assume $\left(a b a^{-1}\right)^{k}=a b^{k} a^{-1}$

For $k=1 \Rightarrow\left(a b a^{-1}\right)=a b a^{-1}$

$\mathrm{k}=2 \Rightarrow\left(\mathrm{ab} \mathrm{a}^{-1}\right)^{2}=\mathrm{ab} \mathrm{a}^{-1} \cdot \mathrm{ab} \mathrm{a}^{-1}$

$true$ abeb $a^{-1} \quad\left[\because a^{-1} \cdot a=e\right]$

$=a b b a^{-1} \quad[\because \quad b \cdot e=b]$

$=a b^{2} a^{-1} \quad\left[\because \quad b \cdot b=b^{2}\right]$

Discrete MathematicsGroup Theory

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Question 43

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Consider the keys , what will be the correct tree structure if min heap is to be created

$true$

Correct answer

none of the above

Solution

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Database Management SystemB-Tree

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Question 44

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The minimum 2 input NAND gate required to implement boolean function

$\mathrm{Y}=\mathrm{P} \overline{\mathrm{Q}} \mathrm{R}+\mathrm{PQ} \mathrm{RS}+\mathrm{P} \overline{\mathrm{Q}} \mathrm{RST}$

Correct answer

Solution

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$Y=P \bar{Q} R+P \bar{Q} R S+P \bar{Q} R S T \\ =P \bar{Q} R+P \bar{Q} R S \\ =P \bar{Q} R$

For a single AND-gate two NAND gates are required, for NOT gate 1 NAND gate is required. So, minimum # NAND gate required for

$\mathrm{Y}=\mathrm{P\bar{Q}} \mathrm{R}$ is equals to $true$

Digital ElectronicsBoolean Algebra

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Question 45

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The computer has 32 bit instruction as shown

Assume there are 205 instruction on machine and 128 register, find number of bits required for immediate field:

Correct answer

Solution

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10-bits required for immediate field.

COAALU,Data-Path & Control Unit

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Question 46

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Which of the following is the primary advantage of double precision.

Greater precision

Correct answer

Increase the exponent range

Represents more numbers

None

Solution

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Although double precision does increase the exponent range, its primary advantage is its greater precision because of the much larger fraction.

Digital ElectronicsNumber System

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Question 47

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The page number in the 24-bit address 0x654321 with an 256-byte page size is:

0x56

0x12

0x6543

Correct answer

0x3456

Solution

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Since a 256-byte page takes 8 bits in VA, rest 24-8=16bits are for page numbers. Each Hexadecimal number requires 4 bits in binary for representation. So In address first 16 bits or 4 Hexa digits is the page number ie. 0X6543. Rest 0x21 is page offset.

Operating SystemMemory Management

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Question 48

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Consider the following grammar where {#, %, x,y} are terminals.

S-> P

P-> QR | TQR

Q->Q# | ϵ

R-> % | ϵ

T-> x | y

Select the correct option.

First(P)={#,x,y,ϵ}

First(P)={#,x,y,%}

First(P)={#,x,y,ϵ}

First(P)={#,x,y,%,ϵ}

Correct answer

Solution

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First(P)= First(QR) U First(TQR)

FIRST(QR)= {#,%,ϵ}

First(TQR)={x,y}

Compiler DesignParsing

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Question 49

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Any graph G is a set of vertices and edges i.e., G=(v,e). Which of the following graphs are planar?

$1. \mathrm{K}_{5}\\ 2. \mathrm{G}_{1}=(12,18)\\ 3. G_{2}=(25,56)$

1, 2, 3

1, 2

2, 3

Correct answer

1, 3

Solution

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If the inequality $e \leq 3 v-6$ is satisfied the graph is planar, else it is non-planar. $K_{5}$ has 5 vertices and 10 edges.

$10>3 \times 5-6$

The inequality is not satisfied therefore it is not planar.

$\begin{aligned} v &=12, e=20 \\ 20 & \leq 3 \times 12-6 \\ 20 & \leq 30 \end{aligned}$

$\therefore$ The graph is planar.

$v=25, t=56 \\ 56 \leq 3 \times 25-6 \\ 56 \leq 69$

Graph 2 and 3 are planar

Discrete MathematicsGroup Theory

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Question 50

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A depth first search on a directed graph can yield which types of edges; tree, forward, back and cross edges

tree edges and cross edges

back edges

forward edges

all of the above

Correct answer

Solution

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A depth first search on a directed graph can yield 4 types of edges; tree, forward, back and cross edges

Consider a directed graph given in below, DFS of the below graph is 1 2 4 6 3 5 7 8. In the diagram below, if DFS is applied on this graph a tree is obtained which is connected using green edges.

Tree Edge: It is an edge which is present in a tree obtained after applying DFS on the graph. All the Green edges are tree edges.

Forward Edge: It is an edge (u, v) such that v is descendant but not part of the DFS tree. Edge from 1 to 8 is a forward edge.

Back edge: It is an edge (u, v) such that v is ancestor of edge u but not part of DFS tree. Edge from 6 to 2 is a back edge.

Cross Edge: It is an edge which connects two nodes such that they do not have any ancestor and a descendant relationship between them. Edge from node 5 to 4 is cross edge.

AlgorithmsGraph Based Algorithm

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Question 51

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RSA algorithm is used by choosing two prime numbers say p=3 and q=11. If the public key is e=3 then what is the value of private key d and what is cipher value of message M=9.

7,3

Correct answer

8,18

11,7

13,17

Solution

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n = p*q = 3*11 = 33,

Φ(n) = (p-1)*(q-1) = 2*10 = 20

d=e-1 mod Φ

=> e*d = 1 mod Φ

=> 3*7 = 1 mod 20 so d=7

$=>\mathrm{d}=7$ now $\mathrm{M}^{\prime}=\mathrm{M}^{e} \bmod \mathrm{n}=9^{3} \bmod 33=3$

Computer NetworkCryptography

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Question 52

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Let a book of 500 pages contain 30 printing mistakes. Let these errors are randomly distributed throughout the book and the number of errors per page has a poisson distribution. The probability that 10 pages selected at random is free from error.

0.6

0.548

Correct answer

0.37

0.52

Solution

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Discrete MathematicsSets

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Question 53

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Consider a pipelined processor having 5 stages. The stage delays are 2, 3, 2.4, 3, 2.5ns and interstage buffer delays are 2ns. The 3rd stage is capable of deciding the branch target address. Processor starts fetching new instructions when the conditional branch outcome is known. 50% of instructions are conditional branch, then calculate the execution time for 1000 instructions?

10000ns

Correct answer

4800ns

6000ns

9000ns

Solution

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5 stage pipeline

Delays are 2, 3, 2.4, 3, 2.5ns

Inter stage buffer delays are 2 ns

Clock cycle time= max stage delay + BUFF delay

= 3 + 2 = 5ns

3rd stage is capable of knowing Branch Address

So number of stall cycles = 2

50% instructions are branch instructions, so stall frequency = 0.50

CPI = (1 + stall Freq * stall cycles) clocks

= (1 + 0.5 * 2) clocks

= 2 clocks

Execution time = 2 * 5 ns / instruction

= 10 ns / instruction

Execution time for 1000 instructions = 10 ns / instruction * 1000 instructions

= 10000 ns

COAPipelining

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Question 54

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Which one of the following statements is / are true about SQL?

SQL permits attribute names to be repeated in the same relation

If there are no indexes on the relations then an SQL query will not work

Duplicates are automatically eliminated by an SQL query

None of the above

Correct answer

Solution

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All the statements about SQL are false

Database Management SystemSQL

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Question 55

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The number of cut-vertex of the following graph is

-

Your answer

5

Correct answer

Solution

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By removing ‘a vertex if the graph will become disconnected, it is called cut-vertex

In the given graph, vertices{ e,f,g,h,i} are the cut-vertices

Network TheoryGraph Theory

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Question 56

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The optimal solution generated by the job sequencing with deadlines with

n = 7

$true$ , $true$ ,... $true$ = (8, 10, 25, 23, 6, 11, 35)

$true$ , $true$ , ..., $true$ = (1, 3, 4, 3, 2, 1, 2) is _____?

-

Your answer

94

Correct answer

Solution

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Total Profit =35+25+23+11=94

AlgorithmsGreedy Techniques

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Question 57

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The number of minterms present in output of following multiplexer

-

Your answer

9

Correct answer

Solution

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Digital ElectronicsCombinational Circuits

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Question 58

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Number of non negative integer solution of equation

$\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\mathrm{x}_{4}+\mathrm{x}_{5}=20$

where $x_{1} \geq-3, x_{2} \geq 0, x_{3} \geq 4, x_{4} \geq 2, x_{5} \geq 2$ is

-

Your answer

3876

Correct answer

Solution

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Let $x_{1}=y_{1}-3, x_{2}=y_{2}, x_{3}=y_{3}+4, x_{4}=y_{4}+2$ and $x_{5}=y_{5}+2$

The given equation becomes $\mathrm{y}_{1}+\mathrm{y}_{2}+\mathrm{y}_{3}+\mathrm{y}_{4}+\mathrm{y}_{5}=15$

The required number of solutions = Number of non-negative integer solutions to the above equation

$=\mathrm{C}(5-1+15,15) \\ =\mathrm{C}(19,15) \\ =\mathrm{C}(19,4) \\ =3876$

Discrete MathematicsSets

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Question 59

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Consider the relation with 5 attributes R(ABCDE), you are given functional dependency

$\mathrm{A} \rightarrow \mathrm{FC}, \mathrm{C} \rightarrow \mathrm{D}, \mathrm{B} \rightarrow \mathrm{E}$

Find the number of relations after converting in 3NF?

-

Your answer

4

Correct answer

Solution

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Key of the given relation is AB and the 3NF relations are $(\mathrm{AB})(\mathrm{ACF})(\mathrm{CD})$ and $(\mathrm{BE})$

Database Management SystemNormalization

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Question 60

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A CNF CFG derives a string of length 5 in _____ steps?

-

Your answer

9

Correct answer

Solution

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A CNF derives a string of length n in 2n-1 steps

Theory of ComputationContext Free Grammar

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Question 61

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Which of the following is true with respect to strict alternation

Which of the following is/are true ?

Always guarantee mutual exclusion

Correct answer

never guarantee progress

Correct answer

Sometimes guarantees bounded waiting but not always

It can cause deadlock

Solution

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Strict alternation implies process to turn while taking CS, hence it always guaranteed progress and deadlock never happens

Operating SystemProcess Synchronization

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Question 62

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