Differential Equations - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2012 · General Aptitude (GA) · General Aptitude · Differential Equations

Mechanical Engineering (ME) 2012

The inverse Laplace transform of the function F(s) = \frac{1}{s(s+1)} is given by

A

f(t) = \sin t

B

f(t) = e^{-t} \sin t

C

f(t) = e^{-t}

D

f(t) = 1 - e^{-t}

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2

2012 · General Aptitude (GA) · General Aptitude · Differential Equations

Mechanical Engineering (ME) 2012

Consider the differential equation $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} - 4y = 0$ with the boundary conditions of $y(0) = 0$ and $y(1) = 1$. The complete solution of the differential equation is

A

x^2

B

\(\sin\left(\frac{\pi x}{2}\right)\)

C

e^x \sin\left(\frac{\pi x}{2}\right)

D

e^{-x} \sin\left(\frac{\pi x}{2}\right)

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3

2015 · General Aptitude (GA) · General Aptitude · Differential Equations

Mechanical Engineering (ME) 2015 [Session 1]

The Blasius equation related to boundary layer theory is a

A

third-order linear partial differential equation

B

third-order nonlinear partial differential equation

C

second-order nonlinear ordinary differential equation

D

third-order nonlinear ordinary differential equation

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4

2015 · General Aptitude (GA) · General Aptitude · Differential Equations

Mechanical Engineering (ME) 2015 [Session 1]

Find the solution of \(\frac{d^2y}{dx^2} = y\) which passes through the origin and the point \(\left(\ln{2}, \frac{3}{4}\right)\)

A

\(y = \frac{1}{2}e^x - e^{-x}\)

B

\(y = \frac{1}{2}(e^x + e^{-x})\)

C

\(y = \frac{1}{2}(e^x - e^{-x})\)

D

\(y = \frac{1}{2}e^x + e^{-x}\)

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5

2015 · General Aptitude (GA) · General Aptitude · Differential Equations

Mechanical Engineering (ME) 2015 [Session 2]

Consider the following differential equation: \[ \frac{dy}{dt} = -5y; \quad \text{initial condition: } y = 2 \text{ at } t = 0. \] The value of \( y \) at \( t = 3 \) is

A

-5e^{-10}

B

2e^{-10}

C

2e^{-15}

D

-15e^{3}

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6

2015 · General Aptitude (GA) · General Aptitude · Differential Equations

Mechanical Engineering (ME) 2015 [Session 2]

The initial velocity of an object is 40 m/s. The acceleration \( a \) of the object is given by the following expression: \[ a = -0.1v, \] where \( v \) is the instantaneous velocity of the object. The velocity of the object after 3 seconds will be ________

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7

2019 · General Aptitude (GA) · General Aptitude · Differential Equations

Mechanical Engineering (ME) 2019 [Session 2]

The differential equation dy/dx+4y-5 is valid in the domain 0≤x≤1 with y(0)=2.25. The solution of the differential equation is

A

y=e^{-4x}+5

B

y=e^{-4x}+1.25

C

y=e^{4x}+5

D

y=e^{4x}+1.25

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