GATE XE topic:engineering PYQs & Answers — Page 2

Questions 11–20 of 1772. Imported answers require independent review unless marked reviewed.

Topic practice 1772 questionsPage 2 of 178

For the complex function

consider the following two statements

is not analytic at

does not satisfy the Cauchy-Riemann equations along the

-axis.

Then, which one of the following statements is true?

Your answerChoose one option.

P is false and Q is true

P is true and Q is false

Both P and Q are true, and Q implies P

Both P and Q are true, but Q does not imply P

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Let

be the circle

oriented counterclockwise. Then, the value of the line integral

Your answerChoose one option.

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Let

denote the Wronskian of two linearly independent solutions

and

of the differential equation

, then the value of

Your answerChoose one option.

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Which of the following statements is/are true?

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

and

are estimated as lines of regression of

and

, respectively.

and

are estimated as lines of regression of

and

, respectively.

and

are estimated as lines of regression of

and

, respectively.

and

are estimated as lines of regression of

and

, respectively, and the correlation between

and

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Consider the matrix

. Then, which of the following statements is/are true?

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

All the eigenvalues of

are real numbers

The eigenvalues of

are

The determinant of

is 3

The matrix

is invertible, where

denotes the identity matrix of order

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Let

be the lamina of the form

, with density

. Then, the mass of

(in integer) is __________

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Let

be a random variable having probability density function (pdf)

Then, the value of the expectation of

(rounded off up to two decimal places) is __________

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Match each entry of List-1 with a suitable entry in List-2 and choose the correct option.

List-1	List-2
P. The sum of the series is equal to	I.
Q. is equal to	II.
R. Let be the Fourier series expansion of the function , . Then, is equal to	III.

Your answerChoose one option.

I, Q

III, R

III, Q

II, R

III, Q

I, R

II, Q

I, R

III

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Consider the following partial differential equation (PDE)

Then, which of the following statements is/are true?

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

In the region

, the PDE is hyperbolic

In the region

, the PDE is elliptic

In the region

, the PDE is elliptic

In the region

, the PDE is hyperbolic

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Let

be the LU decomposition of the matrix

Then, the value of

(in integer) is ________.

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GATE XE topic:engineering PYQs

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20