GATE ECE area:engineering-mathematics PYQs & Answers — Page 9

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Questions 81–90 of 100. Imported answers require independent review unless marked reviewed.

Topic practice 100 questionsPage 9 of 10

The contour C given below is on the complex plane

, where

Diagram for Electronics and Communication Engineering question 51

The value of the integral

is ______.

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Let

and

. Assume that

and

are independent variables. At

, the value (correct to two decimal places) of

is ________ .

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Consider the

matrix

It is given that

has only one real eigenvalue. Then the real eigenvalue of

Your answerChoose one option.

−2.5

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The rank of the matrix

is __________.

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The rank of the matrix

Your answerChoose one option.

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The general solution of the differential equation

in terms of arbitrary constants

and

Your answerChoose one option.

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Consider the following statements about the linear dependence of the real valued functions

and

, over the field of real numbers.

and

are linearly independent on

II.

and

are linearly dependent on

III.

and

are linearly independent on

IV.

and

are linearly dependent on

Which one among the following is correct?

Your answerChoose one option.

Both I and II are true

Both I and III are true

Both II and IV are true

Both III and IV are true

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The smaller angle (in degrees) between the planes

and

is _____.

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Three fair cubic dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces show up is (up to third decimal place) ______.

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The residues of a function

are

Your answerChoose one option.

and

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GATE ECE area:engineering-mathematics PYQs

Question 51

Question 52

Question 1

Question 1

Question 2

Question 2

Question 3

Question 3

Question 4

Question 4