GATE CE Partial Differential Equation (PDE) PYQs & Answers

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Partial Differential Equation (PDE)

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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 Partial Differential Equation (PDE) PYQs

How to practice Partial Differential Equation (PDE)

Question 13

Question 30

Question 13

Question 28

Question 12

Question 28

Question 25

Question 31

Question 52

Question 11