GATE XE exam:gate PYQs & Answers — Page 161

Questions 1601–1610 of 1772. Imported answers require independent review unless marked reviewed.

Topic practice 1772 questionsPage 161 of 178

Consider the ordinary differential equation

where

and

are constants. If

is a solution of the above equation, then the value of

is ________.

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Consider the system of linear equations

The above system has

Your answerChoose one option.

a unique solution

infinite number of solutions

no solution

only two distinct solutions

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Let

be a simple smooth closed curve enclosing the region

in the

-plane. Let

be oriented counterclockwise. If the value of the integral

is 16, then the area of

is ________.

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Consider the ordinary differential equation

In terms of arbitrary constants

and

, the general solution of the above equation is

Your answerChoose one option.

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Let

and

be defined by

where

denotes the set of real numbers. Then, at

Your answerChoose one option.

is differentiable but

is NOT differentiable

is NOT differentiable but

is differentiable

both

and

are differentiable

neither

nor

is differentiable

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is the solution of the wave equation

with the initial conditions

and the boundary conditions

then the value of

is ________.

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Let

where

is a real variable and

. The value of

is ________.

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Let

for

. Then

Your answerChoose one option.

converges but

does NOT converge

does NOT converge but

converges

both

and

converge

neither

nor

converges

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In a given flow field, the velocity vector in Cartesian coordinate system is given as:

What is the volume dilation rate of the fluid at a point where

and

Your answerChoose one option.

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A steady, incompressible, two-dimensional velocity field in Cartesian coordinate system is represented by the following expression.

The coordinates of the point

in the flow field having “zero” velocity is,

Your answerChoose one option.

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GATE XE exam:gate PYQs

Question 4

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Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

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Question 13