Calculus - Engineering Mathematics - Mining Engineering Previous Year Questions

1

2007 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2007

If the slope of a diagonal of a rectangle is $m$ the slope of the other diagonal is

A

$\frac{1}{2m}$

B

$-\frac{1}{2m}$

C

$\frac{1}{m}$

D

$-\frac{1}{m}$

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2

2007 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2007

The functions $f(x)$ and $g(x)$ satisfy $f(x=0)=3$, $f'(x=0)=-5$, $g(x=0)=2$ and $g'(x=0)=-10$. The value of $\frac{d}{dx}\left( \frac{f(x)}{g(x)} \right)_{x=0}$ is

A

-35.0

B

-5.0

C

0.5

D

5.0

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3

2008 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2008

The volume of a cone is given by \[V = \frac{\pi}{3} \ell^3 \sin^2 \theta \cos \theta\] where, ℓ is the slant height and θ is the semi-vertical angle. The angle (θ), for which the volume of cone becomes maximum is

A

\(\sin^{-1}\left(\frac{1}{\sqrt{3}}\right)\)

B

\(\cos^{-1}\left(\frac{1}{\sqrt{3}}\right)\)

C

\(\cos^{-1}(\sqrt{2})\)

D

\(\sin^{-1}(\sqrt{2})\)

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4

2008 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2008

If H is the maximum height attained by a projectile, the maximum horizontal range when fired at 45° inclination from ground level is

A

4.0H

B

3.6H

C

3.2H

D

2.7H

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5

2009 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2009

The value of \( \lim_{x \to 0} \left( \frac{2\sqrt{4-x^2}}{5} \right) \) is

A

\(\frac{2\sqrt{8}}{5} \)

B

0

C

\(\frac{2\sqrt{8}}{5} \)

D

non-existent

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6

2009 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2009

Water starts to flow into a sump initially containing 250 kL of water. The inflow rate of water is 4t L/min where t refers to time elapsed in min. If the pumping rate of water out of the sump is 250 L/min, the total volume of water in the sump after 3 hours in kL is

A

250.5

B

255.6

C

269.8

D

280.9

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7

2009 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2009

There are 50 lemon trees in a reclaimed mine area. Each tree produces 800 lemons per year. For each additional tree planted in this area, considering all trees, the output number of fruits per tree drops by 10 lemons in a year. The number of trees that to be added to the existing reclaimed area in order to maximize the total number of lemons in the year is

A

10

B

15

C

16

D

26

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8

2009 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2009

A 1100 V, 3ϕ power supply system of a mine draws a load of 185 kW. The ammeter reading shows 115 A. The power factor of the system is

A

0.84

B

0.73

C

0.64

D

0.48

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9

2010 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2010

In a Cartesian coordinate system the vertices of a triangular plate are given by (-2, 1), (3, 4), and (-4, -8). The coordinates of the centre of gravity of the plate are

A

3, 4

B

7, 12

C

-1, -1

D

-3, -4

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10

2010 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2010

The value of the \(\lim_{x\to1} [\frac{1 - x^{-1/3}}{1 - x^{-2/3}}]\) is

A

\(\infty\)

B

1

C

0

D

1/2

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11

2010 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2010

The volume of tetrahedron with vertices at (0,0,0), (1,0,0), (0,1,0) and (0,0,1) is

A

1/2

B

1/4

C

1/6

D

1/8

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12

2010 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2010

The value of the given integral is \(\int_{5}^{3x} \frac{\sin x}{(\sin x + \cos x)} dx\)

A

\(\frac{\sin \pi / 8}{10}\)

B

\(\frac{\pi}{10}\)

C

\(\frac{\sin \pi / 5}{10}\)

D

\(\frac{3\pi}{10}\)

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13

2010 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2010

The value of \(k\) for which the points \((5,5),(k,1),(10,7)\) lie on a straight line is

A

-5

B

+5

C

-2

D

+2

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14

2010 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2010

Given the following four functions f₁(n) = n¹⁰⁰, f₂(n) = (1.5)ⁿ, f₃(n) = 2ⁿ/², f₄(n) = 3ⁿ/³ which function will have the largest value for sufficiently large values of n (i.e. n → ∞)?

A

f₄

B

f₃

C

f₂

D

f₁

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15

2011 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2011

The value of \(\lim_{x\to 0} \frac{1}{x} (\sqrt{1+x} - \sqrt{1-x})\) is

A

0

B

1

C

2

D

3

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16

2011 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2011

The infinite series \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots\), is

A

convergent

B

divergent

C

oscillatory

D

semi-convergent

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17

2011 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2011

Value of the integral \(\int_0^1 \sqrt{\frac{1+x}{1-x}} dx\) is

A

\(\frac{\pi}{2} - 1\)

B

\(\frac{\pi}{2} + 1\)

C

\(\pi - 1\)

D

\(\pi + 1\)

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18

2011 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2011

A 1 tonne mine car traveling at a constant speed of 10 km/h collides with a stationary buffer and comes to rest. If the buffer spring stiffness is 200 kN/m, the maximum compression in the spring in mm is

A

49

B

98

C

196

D

247

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19

2011 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2011

An incandescent headlight of a mining vehicle is of spot beam type with a beam angle of 30°. The spherical surface in m² subtended by the lighted beam at a distance of 5 m from the headlight is

A

7.5

B

15

C

21

D

25

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20

2011 · Mining Engineering · Engineering Mathematics · Calculus

Mining Engineering (MN) 2011

The total cost C (lakh rupees) of a longwall face of length L in m is given by the equation
\( C = 0.1L + \frac{1562.5}{L} + 300 \). Length of the face in m for the minimum total cost is

A

40

B

125

C

156

D

300

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