GATE ECE area:engineering-mathematics PYQs & Answers

Home
GATE
Electronics and Communication Engineering
Topics
area:engineering-mathematics

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 100. Imported answers require independent review unless marked reviewed.

Topic practice 100 questionsPage 1 of 10

Consider the differential equation

, with

. If

be the solution to the equation where

and

are unit vectors along the positive x and y axes respectively, then which of the following options is the correct matrix representing A?

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 surface is given by

and

are unit normal vectors to the surface at the point

. Which of the following vectors can be

, where

and

are the unit vectors along x, y and z axes, respectively?

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

Consider the matrix

. Which of the following options is/are TRUE if

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

and

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

Consider the two series,

and

, where

Which of the following statements is correct for the two given series?

Your answerChoose one option.

Both

and

converge.

Neither

nor

converges.

converges but

does not converge.

converges but

does not converge.

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

Let X, N, Y and Z be random variables. The variables X and N are independent of each other. X is uniformly distributed between -1 and 1; N follows Normal distribution with zero mean and unity variance. Y and Z are defined as,

and

. Which of the following pairs represents the values of correlation between X and Y and that between X and Z?

Your answerChoose one option.

1/3 and 0

1/3 and 1/9

1/3 and 1/3

1 and 0

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

Consider the square region

in the X-Y plane as shown with the dark shading in the Figure. The value of

is ___. (rounded off to two decimal places)

Diagram for Electronics and Communication Engineering question 61

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

Consider the matrix

below:

For which of the following combinations of

and

, is the rank of

at least three?

(i)

and

(ii)

(iii)

and

(iv)

Your answerChoose one option.

Only (i), (iii), and (iv)

Only (iv)

Only (ii)

Only (i) and (iii)

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

Consider the following series:

(i)

(ii)

(iii)

Choose the correct option.

Your answerChoose one option.

Only (ii) converges

Only (ii) and (iii) converge

Only (iii) converges

All three converge

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

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.

What is the probability that the two balls drawn have different colours?

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

Consider the function

, defined as

Which of the following statements is/are correct?

(Here,

is the set of real numbers.)

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

has no global maximizer

has no global minimizer

is a local minimizer of

is a local maximizer of

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

GATE ECE area:engineering-mathematics PYQs

How to practice area:engineering-mathematics

Question 11

Question 12

Question 26

Question 36

Question 38

Question 61

Question 11

Question 12

Question 13

Question 25