GATE ECE area:engineering-mathematics PYQs & Answers — Page 3

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Questions 21–30 of 100. Imported answers require independent review unless marked reviewed.

Topic practice 100 questionsPage 3 of 10

Let

be a complex variable. If

and

is the circle in the complex plane with

then

is ______.

Your answerChoose one option.

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Let

, and

be functions of

. Suppose that for every given pair of points

and

in space, the line integral

evaluates to the same value along any path

that starts at

and ends at

. Then which of the following is/are true?

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

For every closed path

, we have

There exists a differentiable scalar function

such that

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Consider the matrix

, where

is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?

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

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Let

and

be two vectors. The value of the coefficient

in the expression

, which minimizes the length of the error vector

, is

Your answerChoose one option.

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The rate of increase, of a scalar field

, in the direction

at a point

Your answerChoose one option.

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Let

. Which of the following cannot be a value of

Your answerChoose one option.

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The value of the contour integral

, where the contour

, taken in the counter clockwise direction, is

Your answerChoose one option.

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Let the sets of eigenvalues and eigenvectors of a matrix

and

, respectively. For any invertible matrix

, the sets of eigenvalues and eigenvectors of the matrix

, where

, respectively, are

Your answerChoose one option.

and

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A random variable

, distributed normally as

, undergoes the transformation

, given in the figure. The form of the probability density function of

(In the options given below,

are non-zero constants and

is piece-wise continuous function)

Diagram for Electronics and Communication Engineering question 36

Your answerChoose one option.

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The value of the line integral

along the straight line joining the points

and

Your answerChoose one option.

-5

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GATE ECE area:engineering-mathematics PYQs

Question 43

Question 54

Question 55

Question 11

Question 12

Question 13

Question 14

Question 15

Question 36

Question 37