GATE CSE year:2017 PYQs & Answers — Page 7

Questions 61–70 of 130. Imported answers require independent review unless marked reviewed.

Let

be an

real valued square symmetric matrix of rank 2 with

. Consider the following statements.

(I) One eigenvalue must be in

(II) The eigenvalue with the largest magnitude must be strictly greater than 5

Which of the above statements about eigenvalues of

is/are necessarily CORRECT?

Your answerChoose one option.

Both (I) and (II)

(I) only

(II) only

Neither (I) nor (II)

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For any discrete random variable

, with probability mass function

, and

, define the polynomial function

. For a certain discrete random variable

, there exists a scalar

such that

. The expectation of

Your answerChoose one option.

Not expressible in terms of

and

alone

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A computer network uses polynomials over

for error checking with 8 bits as information bits and uses

as the generator polynomial to generate the check bits. In this network, the message 01011011 is transmitted as

Your answerChoose one option.

0101101010

0101101011

0101101101

0101101100

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Consider the following expression grammar

E − T | T

T + F | F

(E) | id

Which of the following grammars is not left recursive, but is equivalent to

Your answerChoose one option.

E → E − T | T T → T + F | F F → (E) | id

E → TE′ E′ → −TE′ | ε T → T + F | F F → (E) | id

E → TX X → −TX | ε T → FY Y → +FY | ε F → (E) | id

E → TX | (TX) X → −TX | +TX | ε T → id

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Consider a combination of T and D flip-flops connected as shown below. The output of the D flip-flop is connected to the input of the T flip-flop and the output of the T flip-flop is connected to the input of the D flip-flop.

Diagram for Computer Science and Information Technology question 33

Initially, both Q₀ and Q₁ are set to 1 (before the 1st clock cycle). The outputs

Your answerChoose one option.

Q₁Q₀ after the 3rd cycle are 11 and after the 4th cycle are 00 respectively

Q₁Q₀ after the 3rd cycle are 11 and after the 4th cycle are 01 respectively

Q₁Q₀ after the 3rd cycle are 00 and after the 4th cycle are 11 respectively

Q₁Q₀ after the 3rd cycle are 01 and after the 4th cycle are 01 respectively

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A system shares 9 tape drives. The current allocation and maximum requirement of tape drives for three processes are shown below:

Process	Current Allocation	Maximum Requirement
P1	3	7
P2	1	6
P3	3	5

Which of the following best describes current state of the system?

Your answerChoose one option.

Safe, Deadlocked

Safe, Not Deadlocked

Not Safe, Deadlocked

Not Safe, Not Deadlocked

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is a grammar with productions

where

is the start variable, then which one of the following strings is not generated by

Your answerChoose one option.

abab

aaab

abab

baba

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Consider a binary code that consists of only four valid codewords as given below:

00000, 01011, 10101, 11110

Let the minimum Hamming distance of the code be

and the maximum number of erroneous bits that can be corrected by the code be

. Then the values of

and

are

Your answerChoose one option.

and

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Consider the following two functions.

void fun1(int n) {

if(n == 0) return;

printf("%d", n);

fun2(n - 2);

printf("%d", n);

}

void fun2(int n) {

if(n == 0) return;

printf("%d", n);

fun1(++n);

printf("%d", n);

}

The output printed when fun1(5) is called is

Your answerChoose one option.

54323122233445

54323120112233

5432312213245

54323120213243

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Consider two hosts

and

, connected by a single direct link of rate

bits/sec. The distance between the two hosts is 10,000 km and the propagation speed along the link is

m/sec. Host

sends a file of 50,000 bytes as one large message to host

continuously. Let the transmission and propagation delays be

milliseconds and

milliseconds, respectively. Then the values of

and

are

Your answerChoose one option.

and

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GATE CSE year:2017 PYQs

Question 31

Question 31

Question 32

Question 32

Question 33

Question 33

Question 34

Question 34

Question 35

Question 35