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

2010 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2010

The Laplace transformation of t³e^4t is

A

\(\frac{4!}{(s-3)^4}\)

B

\(\frac{3!}{(s-4)^4}\)

C

\(\frac{3!}{(s-4)^3}\)

D

\(\frac{4!}{(s-4)^3}\)

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11

2010 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2010

The derivative of \(y = \sqrt{x + \sqrt{x + \sqrt{x + ...}}}\) with respect to x at y = 0 is

A

-1

B

0

C

1

D

2

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12

2010 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2010

The value of \(\int_{0}^{2} \int_{0}^{1} xy \, dx \, dy\) is

A

0.5

B

1.0

C

2.0

D

4.0

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13

2010 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2010

Which of the following options is the closest in meaning to the word below:
Circuitous

A

cyclic

B

indirect

C

confusing

D

crooked

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14

2010 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2010

If 137 + 276 = 435 how much is 731 + 672?

A

534

B

1403

C

1623

D

1513

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15

2011 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2011

The mean value of a function \(f(x)\) from \(x = a\) to \(x = b\) is given by

A

\(\frac{f(a)+f(b)}{2}\)

B

\(\frac{f(a)+2f\left(\frac{a+b}{2}\right)+f(b)}{4}\)

C

\(\int_a^b f(x)dx\)

D

\(\frac{\int_a^b f(x)dx}{(b-a)}\)

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16

2011 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2011

The stationary points of \(f(x, y) = \frac{1}{3}x^3 - xy^2 - 2y\) are

A

(1,–1) and (–1,1)

B

(1,1) and (–1,–1)

C

(2,–2) and (–2,2)

D

(2,2) and (–2,–2)

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17

2011 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2011

The sum of n terms of the series 4+44+444+.... is

A

(4/81) [10^{n+1} – 9n – 1]

B

(4/81) [10^{n-1} – 9n – 1]

C

(4/81) [10^{n+1} – 9n – 10]

D

(4/81) [10^{n} – 9n – 10]

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18

2011 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2011

Given that f(y) = | y | / y, and q is any non-zero real number, the value of | f(q) – f(-q) | is

A

0

B

-1

C

1

D

2

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19

2011 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2011

Three friends, R, S and T shared toffee from a bowl. R took 1/3rd of the toffees, but returned four toffees to the bowl. S took 1/4th of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees were originally there in the bowl?

A

38

B

31

C

48

D

41

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20

2013 · Agricultural Engineering · Engineering Mathematics · Calculus

Agricultural Engineering (AG) 2013

If \( 3 \le X \le 5 \) and \( 8 \le Y \le 11 \) then which of the following options is TRUE?

A

\(\frac{3}{5} \le \frac{X}{Y} \le \frac{8}{5} \)

B

\(\frac{3}{11} \le \frac{X}{Y} \le \frac{5}{8} \)

C

\(\frac{3}{11} \le \frac{X}{Y} \le \frac{8}{5} \)

D

\(\frac{3}{5} \le \frac{X}{Y} \le \frac{8}{11} \)

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