GATE XE year:2021 PYQs & Answers — Page 2

Questions 11–20 of 175. Imported answers require independent review unless marked reviewed.

Topic practice 175 questionsPage 2 of 18

Let

, then the value of

Your answerChoose one option.

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Let

be the boundary of the region

in the

-plane and

be the area of the region

. If

traverses once in the counter clockwise direction, then the value of the line integral

is equal to

Your answerChoose one option.

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Given that

. The value of

Your answerChoose one option.

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Let

be a non-negative continuous function of real variable

. If the area under the curve

from

, then the value of

is ______ (round off to one decimal place).

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If the numerical approximation of the value of the integral

using the Trapezoidal rule with two subintervals is 9, then the value of the real constant

is ______ (round off to one decimal place).

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Let the transformation

reduce the ordinary differential equation

where

are real constants. Then, the arithmetic mean of

is ______ (round off to three decimal places).

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A person, who speaks the truth 3 out of 4 times, throws a fair dice with six faces and informs that the outcome is 5. The probability that the outcome is really 5 is ________ (round off to three decimal places).

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Let

be a real valued function. Then, which one of the following statements is TRUE for all

Your answerChoose one option.

is not a stationary point of

has a local maxima at

has a local minima at

has a saddle point at

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Let

be such that both

and

satisfy the Laplace equation in a domain

of the

-plane. Then, which one of the following is TRUE in

Your answerChoose one option.

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Let

denote the identity matrix of order 7, and

be a

real matrix having characteristic polynomial

, where

and

are positive integers. If

is diagonalizable and

, then

is ______ (in integer).

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GATE XE year:2021 PYQs

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10