GATE CSE topic:engineering-mathematics PYQs & Answers — Page 5

Questions 41–50 of 55. Imported answers require independent review unless marked reviewed.

The value of

correct to three decimal places (assuming that

) is ____.

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Consider a matrix

where

. Note that

denotes the transpose of

. The largest eigenvalue of

is ____.

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The chromatic number of the following graph is ______.

Diagram for Computer Science and Information Technology question 18

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Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is ______.

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Consider a matrix P whose only eigenvectors are the multiples of

Consider the following statements.

(I) P does not have an inverse (II) P has a repeated eigenvalue (III) P cannot be diagonalized

Which one of the following options is correct?

Your answerChoose one option.

Only I and III are necessarily true

Only II is necessarily true

Only I and II are necessarily true

Only II and III are necessarily true

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Let N be the set of natural numbers. Consider the following sets. P: Set of Rational numbers (positive and negative) Q: Set of functions from to N R: Set of functions from N to S: Set of finite subsets of N. Which of the sets above are countable?

Your answerChoose one option.

Q and S only

P and S only

P and R only

P, Q and S only

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Let G be a graph with

vertices, with each vertex labelled by a distinct permutation of the numbers 1, 2, ..., 100. There is an edge between vertices

and

if and only if the label of

can be obtained by swapping two adjacent numbers in the label of

. Let y denote the degree of a vertex in G, and z denote the number of connected components in G. Then,

_____.

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Consider Guahati (G) and Delhi (D) whose temperatures can be classified as high (H), medium (M) and low (L). Let

denote the probability that Guahati has high temperature. Similarly,

and

denote the probability of Guahati having medium and low temperatures respectively. Similarly, we use

and

for Delhi.

The following table gives the conditional probabilities for Delhi’s temperature given Guwahati’s temperature.


0.40	0.48	0.12
0.10	0.65	0.25
0.01	0.50	0.49

Consider the first row in the table above. The first entry denotes that if Guwahati has high temperature (

) then the probability of Delhi also having a high temperature (

) is 0.40; i.e.,

. Similarly, the next two entries are

and

. Similarly for the other rows.

If it is known that

, and

, then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _____.

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Let

denote the statements “It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold” is represented by

Your answerChoose one option.

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Consider the set

under the partial ordering

. The Hasse diagram of the partial order

is shown below.

Diagram for Computer Science and Information Technology question 21

The minimum number of ordered pairs that need to be added to

to make

a lattice is __________.

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GATE CSE topic:engineering-mathematics PYQs

Question 16

Question 17

Question 18

Question 19

Question 26

Question 27

Question 43

Question 44

Question 11

Question 21