GATE MT topic:differential-equations PYQs & Answers

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topic:differential-equations

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

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

Topic practice 10 questionsPage 1 of 1

Given a function

, where

is a constant. The Laplace transform of the function is

. Which one of the following options is correct?

Your answerChoose one option.

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Solution of the differential equation

where

. The value of

(answer in integer) is ________________

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For two continuous functions

and

, the relation

describes an exact differential equation if

Your answerChoose one option.

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, then

Your answerChoose one option.

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Order (O) and degree (D) of the differential equation

are

Your answerChoose one option.

O = 2 and D = 1

O = 1 and D = 2

O = 6 and D = 1

O = 2 and D = 6

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The general solution to the following differential equation is _________, where A and B are constants

Your answerChoose one option.

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The general solution to the following homogeneous ODE,

is,

The values of

and

are:

Your answerChoose one option.

-1 and -3

-3 and -3

1 and -3

1 and 3

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Steady state radial heat conduction through a hollow, infinitely long zirconia cylinder is governed by the following ordinary differential equation:

Here, T is the temperature and r is the radial distance. The inner surface of the hollow cylinder is maintained at 1473 K and the outer surface at 973 K. The rate of heat loss per unit length through the outer surface of the hollow cylinder (in W.m⁻¹, rounded off to the nearest integer) is _____________.

Given: Inner radius of cylinder = 0.05 m; outer radius of cylinder = 0.07 m and thermal conductivity of zirconia (k) = 2 W.m⁻¹.K⁻¹.

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Consider the following Ordinary Differential Equation:

In a domain

, with boundary conditions

and

, pick the appropriate choice for

from the following options:

Your answerChoose one option.

Diagram for Metallurgical Engineering question 35

Diagram for Metallurgical Engineering question 35 (figure 2)

Diagram for Metallurgical Engineering question 35 (figure 3)

Diagram for Metallurgical Engineering question 35 (figure 4)

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For the second order linear ordinary differential equation,

, the following function is a solution:

. Which one of the following statements is NOT TRUE?

Your answerChoose one option.

has two values: one complex and one real

has two real values

has two complex values

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GATE MT topic:differential-equations PYQs

How to practice topic:differential-equations

Question 11

Question 46

Question 36

Question 37

Question 13

Question 36

Question 1

Question 41

Question 35

Question 29