GATE MA Partial Differential Equations PYQs & Answers — Page 4

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Questions 31–39 of 39. Imported answers require independent review unless marked reviewed.

Topic practice 39 questionsPage 4 of 4

The partial differential equation

Your answerChoose one option.

parabolic in the region

hyperbolic in the region

elliptic in the region

hyperbolic in the region

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Consider the following heat conduction problem for a finite rod

with the boundary conditions

and the initial condition

. If

, then which one of the following is CORRECT?

Your answerChoose one option.

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The general integral of the partial differential equation

is given by

, where

is a continuously differentiable function.

(

is the set of all real numbers and

)

Then which one of the following is TRUE?

Your answerChoose one option.

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A solution of the Dirichlet problem

is given by

Your answerChoose one option.

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The Cauchy problem

with

, when solved using its characteristic equations with an independent variable

, is found to admit of a solution in the form

Then

Your answerChoose one option.

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If the characteristic curves of the partial differential equation

are

and

, where

and

are constants, then

Your answerChoose one option.

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The partial differential equation

Your answerChoose one option.

hyperbolic along the line

elliptic along the line

parabolic along the line

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Let

be the solution of

satisfying the condition

on the circle

. Then

equals ________.

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Let

be the bounded solution of the following boundary value problem in polar coordinates:

Then

equals

Your answerChoose one option.

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GATE MA Partial Differential Equations PYQs

Question 4

Question 29

Question 31

Question 33

Question 10

Question 33

Question 18

Question 43

Question 44