Calculus - Engineering Mathematics - Agricultural Engineering Previous Year Questions

1

2007 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2007

\(\frac{\omega}{(s+a)^2+\omega^2}\) is the Laplace Transform of

A

\(\exp(-at) \sin \omega t\)

B

\(\exp(-at) \sinh \omega t\)

C

\(at \sin \omega t\)

D

\(at \sinh \omega t\)

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2

2008 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2008

Integration of \(\int_{0}^{\pi/2} \frac{\cos \theta d\theta}{\sqrt{1-\cos^2 \theta}}\) is

A

0

B

\(\pi/2\)

C

1

D

\(\pi\)

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3

2008 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2008

If log(y) = x log_e(x), then the maximum value of y is

A

e

B

\(e^{e^2}\)

C

\(e^{e^{-1}}\)

D

\(e^{-1}\)

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4

2008 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2008

Inverse Laplace Transform of 1/(s – 2)² is

A

\(\exp(2t)\)

B

\(t \exp(2t)\)

C

\(2t \exp(t)\)

D

\(t^2 \exp(2t)\)

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5

2008 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2008

Cycloid is formed by x = a(θ – cos θ) and y = a(1 – cos θ). The surface area of the curved plane obtained from the rotation of the cycloid around x axis is

A

\(\frac{16\pi a^2}{3}\)

B

\(\frac{32\pi a^2}{3}\)

C

\(\frac{64\pi a^2}{3}\)

D

\(\frac{128\pi a^2}{3}\)

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6

2008 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2008

If \(\sum_{i=1}^{n} (x - a_i)^2\) has a minima at A, then A is the arithmetic mean of the series

A

\(a_1 - a_2 + a_3 - ... + (-1)^{n+1} a_n\)

B

\(\frac{1}{a_1} + \frac{1}{a_2} + \frac{1}{a_3} + ... + \frac{1}{a_n}\)

C

\(\frac{1}{a_1} - \frac{1}{a_2} + \frac{1}{a_3} - ... + (-1)^{n+1} \frac{1}{a_n}\)

D

\(a_1 + a_2 + a_3 + ... + a_n\)

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7

2009 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2009

\(I = \int_{0}^{\pi/2} \frac{\cos x \, dx}{(1 + \sin x)^2}\) is

A

-0.5

B

0

C

0.5

D

1

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8

2009 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2009

A curve is having the equation, r = a(1 – cos θ). The perimeter of the curve between θ = 0 to 2π is

A

2a

B

4a

C

6a

D

8a

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9

2009 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2009

\(\frac{1}{s^2 - a^2}\) is the Laplace Transform of

A

\(\sin at\)

B

\(t \sin at\)

C

\(\sinh at\)

D

\(a^{-1} \sinh at\)

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10

2026 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2026

The value of the integral \( I = \int_0^1 \int_0^1 x \cos(xy) \, dx \, dy \) is

A

\(1 - \cos(1) \)

B

\(1 + \cos(1) \)

C

\(1 - \sin(1) \)

D

\(1 + \sin(1) \)

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