GATE CE topic:partial-differential-equations PYQs & Answers

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topic:partial-differential-equations

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Questions 1–10 of 19. Imported answers require independent review unless marked reviewed.

Topic practice 19 questionsPage 1 of 2

Periodic function

is given below.

The CORRECT option representing the Fourier series expansion of

is:

Your answerChoose one option.

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A partial differential equation is given below.

Possible solution(s) is/are:

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

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Which one of the following options is the correct Fourier series of the periodic function

described below:

Your answerChoose one option.

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Which of the following equations belong/belongs to the class of second-order, linear, homogeneous partial differential equations:

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

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The second-order differential equation in an unknown function

is defined as

Assuming

, and

, the general solution of the above differential equation is

Your answerChoose one option.

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For the following partial differential equation,

which of the following option(s) is/are CORRECT?

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

elliptic for x > 0 and y > 0

parabolic for x > 0 and y > 0

elliptic for x = 0 and y > 0

hyperbolic for x < 0 and y > 0

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The following function is defined over the interval

If it is expressed as a Fourier series,

which options amongst the following are true?

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

depend on

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The steady-state temperature distribution in a square plate ABCD is governed by the 2-dimensional Laplace equation. The side AB is kept at a temperature of 100 °C and the other three sides are kept at a temperature of 0 °C. Ignoring the effect of discontinuities in the boundary conditions at the corners, the steady-state temperature at the center of the plate is obtained as T₀ °C. Due to symmetry, the steady-state temperature at the center will be same (T₀ °C), when any one side of the square is kept at a temperature of 100 °C and the remaining three sides are kept at a temperature of 0 °C. Using the principle of superposition, the value of T₀ is __________ (round off to two decimal places).

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A 5 cm long metal rod AB was initially at a uniform temperature of

°C. Thereafter, temperature at both the ends are maintained at 0 °C. Neglecting the heat transfer from the lateral surface of the rod, the heat transfer in the rod is governed by the one-dimensional diffusion equation

, where D is the thermal diffusivity of the metal, given as 1.0 cm²/s.

The temperature distribution in the rod is obtained as

where x is in cm measured from A to B with

at A, t is in s,

are constants in °C, T is in °C, and

is in s⁻¹.

The value of

(in s⁻¹, rounded off to three decimal places) is ____________.

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Consider the following expression:

where

, and

are variables, and

is a complex number. The partial differential equation derived from the above expression is

Your answerChoose one option.

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GATE CE topic:partial-differential-equations PYQs

How to practice topic:partial-differential-equations

Question 13

Question 30

Question 13

Question 28

Question 12

Question 28

Question 25

Question 31

Question 52

Question 11