GATE ES area:engineering-mathematics PYQs & Answers

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 57. Imported answers require independent review unless marked reviewed.

Topic practice 57 questionsPage 1 of 6

, then

is ______.

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The correct integral of

(assuming integral constant as c) is ______.

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Given

, the minimum value of

is ______.

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A box contains 26 cards with all English alphabets from A to Z. The probability of randomly choosing the card with either ‘E’ or ‘S’ from this box is ______.

Your answerChoose one option.

2/26

1/26

3/26

4/26

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Which ONE of the following options is the CORRECT formula for Chi-Square (

) test?

Given,

are the observed values,

are the corresponding expected values,

is the mean of observed values,

is the number of observations,

is the mean of

is the standard deviation of observed values, and

is the standard deviation of expected values

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A 6-hour rainfall of 6 cm at a station was found to have a return period of 40 years. The probability that a 6-hour rainfall of this or larger magnitude will occur at least once in 20 successive years at that station is ______ (rounded off to three decimal places).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A first-order ordinary differential equation is given as follows:

Which ONE of the following options CORRECTLY represents the characteristics of this equation?

Your answerChoose one option.

Linear, homogeneous, and exact

Nonlinear, nonhomogeneous, and exact

Linear, homogeneous, and non-exact

Nonlinear, nonhomogeneous, and non-exact

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the matrix

. Which ONE of the following options CORRECTLY lists the eigenvalues of

Your answerChoose one option.

1; 8 −

; −8 +

2; 8 −

; −8 +

1; 8 +

; 8 −

2; 8 +

; 8 +

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A system of linear equations is given as

, where

, and

is the solution vector. Which of the following statements is/are TRUE for this system?

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

Matrix

is skew-symmetric.

Eigenvalues of matrix

are real.

The system is homogeneous.

The system is singular.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The area in the first quadrant bounded by the function

and the coordinate axes is _____ square units (answer in integer).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE ES area:engineering-mathematics PYQs

How to practice area:engineering-mathematics

Question 11

Question 12

Question 13

Question 14

Question 15

Question 34

Question 36

Question 37

Question 42

Question 64