GATE MA Partial Differential Equations PYQs & Answers — Page 3

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Questions 21–30 of 39. Imported answers require independent review unless marked reviewed.

Topic practice 39 questionsPage 3 of 4

Let

be the solution of the wave equation

with the initial conditions

and the boundary conditions

. Then, the value of

Your answerChoose one option.

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If the Laplace equation

with the boundary conditions

and

has a solution, then the constant

is _____.

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Let

be the solution of the first order partial differential equation

satisfying

. Then, the value of

is _____.

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The function

satisfies the initial value problem

Then

Your answerChoose one option.

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Consider the second-order partial differential equation (PDE)

Consider the following statements: P: The PDE is parabolic on the ellipse

. Q: The PDE is hyperbolic inside the ellipse

. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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is the solution for the Cauchy problem

then

is equal to

Your answerChoose one option.

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solves the following initial boundary value problem

then

__________.

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Let

be a function such that the solution of the initial value problem

is given by

for all bounded continuous functions

. Then the value of

is ________

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Let

be the solution of

, where

is a twice continuously differentiable function. If

, and

, then the value of

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Let

be the solution of the initial value problem

Then the value of

is (rounded off to three decimal places)

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GATE MA Partial Differential Equations PYQs

Question 46

Question 61

Question 62

Question 7

Question 27

Question 28

Question 51

Question 14

Question 25

Question 54