GATE CSE Engineering Mathematics PYQs & Answers

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Revise discrete mathematics, linear algebra and probability with assumptions stated before computation.

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 55. Imported answers require independent review unless marked reviewed.

Topic practice 55 questionsPage 1 of 6

For positive real numbers

and

, the function

is defined as:

. The max function is defined as:

The graph below shows the plot of a function

versus

can be expressed as _____.

Diagram for Computer Science and Information Technology question 8

Your answerChoose one option.

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An urn contains one red ball and one blue ball. At each step, a ball is picked uniformly at random from the urn, and this ball together with another ball of the same color is put back in the urn. The probability that there are equal number of red and blue balls after two steps is

Your answerChoose one option.

1/4

1/3

1/2

2/3

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For two different persons

and

, the predicate

denotes that x knows y. Consider the following statement.

There is a person who does not know anyone else, but that person is known by everyone else.

Which one of the following expressions represents the above statement?

Your answerChoose one option.

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Consider

matrices with their elements from

. The number of such matrices with even number of 1s in every row and every column is

Your answerChoose one option.

512

1025

1023

255

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For

, the maximum multiplicity of any eigenvalue of an

matrix with elements from

Your answerChoose one option.

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The probability density function

of a random variable

which takes real values is

Which one of the following statements is correct about the random variable

Your answerChoose one option.

is an exponential random variable

is a normal random variable

is a Poisson random variable

is a uniform random variable

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Let

. Consider an

matrix

with its elements from

. Let the vector

be in the null space of

Which of the following options is/are always correct?

Your answerSelect all correct options. You can choose more than one.

Determinant of

is 1

Determinant of

is 0

Rank of

is 1

There are at least two non-zero vectors in the null space of

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Let

be a binary relation on the set

, where

if the product of

and

is square of an integer. Which of the following properties is/are satisfied by

Your answerSelect all correct options. You can choose more than one.

Reflexive

Symmetric

Transitive

Antisymmetric

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For a real number

, let

. Which of the following statements is/are true?

Your answerSelect all correct options. You can choose more than one.

The value of

is independent of the value of

The value of

can vary with the value of

There exists

such that

is a positive real number

There exists

such that

is a negative real number

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Consider the system of linear equations given below.

Suppose the values of a and b are chosen such that the system of linear equations produce multiple solutions. Then the product of a and b is __________. (answer in integer)

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GATE CSE Engineering Mathematics PYQs

How to practice Engineering Mathematics

Question 8

Question 11

Question 11

Question 12

Question 13

Question 14

Question 20

Question 26

Question 27

Question 31