GATE AE topic:differential-equations PYQs & Answers

Home
GATE
Aerospace Engineering
Topics
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 23. Imported answers require independent review unless marked reviewed.

Topic practice 23 questionsPage 1 of 3

The following equation with respect to

, where

is a non-zero constant, represents ________.

Your answerChoose one option.

linear wave propagation

transient heat conduction

Newton’s law of cooling

radiative transfer

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the differential equation with the initial conditions given below. If

is the solution of the equation, the value of the slope,

, at

is ________ (rounded off to three decimal places).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

An object of mass 1 kg is launched with an initial speed of

into a large tank filled with a viscous liquid. The liquid exerts a resistive force (drag) of the form

on any object that is moving inside it, where

is the instantaneous speed of the object and

kg/s. If the effect of gravity is ignored, the time taken by the object to slow down to the speed

is ________ s (rounded off to 2 decimal places).

Assume that the tank is sufficiently large for the above deceleration to happen inside the tank.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The partial differential equation

is _____.

Your answerChoose one option.

elliptic

hyperbolic

parabolic

of mixed type

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the ordinary differential equation:

. If

, then the value of

(rounded off to the nearest integer).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The acceleration of a body traveling in a straight line is given by

where

is the velocity, and

are positive constants. Starting with an initial positive velocity

, the distance traveled by the body before coming to rest for the first time is:

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Given

, where

and

are non-zero real numbers, the value of the differential expression

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the one-dimensional wave equation

for

. For an initial condition

, the solution at

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the equation

, where

and

are constants. Given

, select all correct statement(s) from the following as

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

;

is a constant

;

and

are constants

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the differential equation

with initial conditions

. The value of y at

is _____. (round off to two decimal places)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE AE topic:differential-equations PYQs

How to practice topic:differential-equations

Question 13

Question 49

Question 50

Question 14

Question 43

Question 12

Question 36

Question 13

Question 42

Question 54