GATE CSE area:engineering-mathematics PYQs & Answers — Page 10

Questions 91–100 of 109. Imported answers require independent review unless marked reviewed.

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

be scalars, not all zero, such that

where

are column vectors in

. Consider the set of linear equations

where

and

. The set of equations has

Your answerChoose one option.

a unique solution at

where

denotes a

-dimensional vector of all 1

no solution

infinitely many solutions

finite many solutions

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and

, then the constants

and

are, respectively

Your answerChoose one option.

and

and 0

and

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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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Let X be a Gaussian random variable with mean 0 and variance σ². Let Y = max(X, 0) where max(a, b) is the maximum of a and b. The median of Y is __________.

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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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Let

and

be two matrices. Then the rank of

is __________.

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is an undirected graph with

vertices and 25 edges such that each vertex of

has degree at least 3. Then the maximum possible value of

is __________.

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Consider a quadratic equation

with coefficients in a base

. The solutions of this equation in the same base

are

and

. Then

__________.

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GATE CSE area:engineering-mathematics PYQs

Question 43

Question 44

Question 3

Question 10

Question 11

Question 19

Question 21

Question 22

Question 23

Question 24