Calculus - Engineering Mathematics - Metallurgical Engineering Previous Year Questions

1

2008 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2008

\(\int \frac{dx}{a+bx}\) is

A

\(\frac{1}{b} \ln(a+bx)+c\)

B

\(\ln(a+bx)+c\)

C

\(b \ln(a+bx)+c\)

D

\(\frac{1}{a} \ln(a+bx)+c\)

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2

2009 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2009

The function, \( f(x) = ax^2 + bx + c \) has a maxima only if

A

\(a < 0 \)

B

\(a > 0 \)

C

\(a = 0 \)

D

\(a > 0 \) and \(b < 0 \)

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3

2009 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2009

\( \lim_{x \to 0} \frac{\sin x}{x} \) is equal to

A

0

B

1

C

∞

D

undefined

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4

2009 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2009

Taylor series can be used to approximate the value of \(f(x) = \cos x\) by expanding around \(x = 0\). If only the first three terms of the series are considered, the magnitude of deviation from the actual value of \(\cos (\pi/3)\) will be

A

0.01

B

0.03

C

0.05

D

0.07

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5

2010 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2010

Determine the radius (in m) of a cylinder of volume 200 m³ that has the least surface area

A

2.302

B

3.142

C

3.169

D

7.233

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6

2010 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2010

The lim_{x→0} \frac{\sin² a x}{\sin² x} is

A

a²

B

0

C

1

D

undefined

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7

2010 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2010

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

A

534

B

1403

C

1623

D

1513

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8

2011 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2011

The inflection point of a nonlinear function U(r) is at

A

U = 0

B

ln U = 0

C

dU/dr = 0

D

d²U/dr² = 0

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9

2011 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2011

\( Y = k_1 \left[ 1 - \exp \left( - \frac{k_2 \Delta X}{k_3 X} \right) \right] \), where \( k_1 \), \( k_2 \) and \( k_3 \) are constants. If \( k_2 \Delta X << k_3 X \), the value of \( Y \) up to first order of approximation would be

A

\(Y = k_1 \left[ 1 - \frac{k_2 \Delta X}{k_3 X} \right] \)

B

\(Y = k_1 \left[ 1 + \frac{k_2 \Delta X}{k_3 X} \right] \)

C

\(Y = k_1 \frac{k_2 \Delta X}{k_3 X} \)

D

\(Y = -k_1 \frac{k_2 \Delta X}{k_3 X} \)

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10

2011 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 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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11

2011 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2011

Three friends, R, S and T shared toffee from a bowl. R took 1/3^rd of the toffees, but returned four to the bowl. S took 1/4^th 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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12

2011 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2011

The fuel consumed by a motorcycle during a journey while traveling at various speeds is indicated in the graph below.

The distances covered during four laps of the journey are listed in the table below:

Lap	Distance (kilometres)	Average speed (kilometres per hour)
P	15	15
Q	75	45
R	40	75
S	10	10

From the given data, we can conclude that the fuel consumed per kilometre was least during the lap

A

P

B

Q

C

R

D

S

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13

2011 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2011

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

A

(4/81) [10ⁿ⁺¹ - 9n - 1]

B

(4/81) [10^n-1 - 9n - 1]

C

(4/81) [10ⁿ⁺¹ - 9n - 10]

D

(4/81) [10ⁿ - 9n - 10]

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14

2012 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2012

At x = 0.5, the polynomial x²(1-x)² has

A

No extrema

B

A saddle point

C

A minima

D

A maxima

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15

2012 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2012

The temperature field of a slab is given by T = 400 – 50z exp (–t – x² – y²). The temperature gradient in y-direction is

A

100yz exp(–t – x² – y²)

B

–100yz exp(–t – x² – y²)

C

100xz exp(–t – x² – y²)

D

–100xz exp(–t – x² – y²)

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16

2013 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2013

Which one of the following series is divergent?

A

\(\sum_{n=1}^{\infty} \frac{1}{3^{n-1}} \)

B

\(\sum_{n=1}^{\infty} \frac{1}{n} \)

C

\(\sum_{n=1}^{\infty} \frac{1}{2^n} \)

D

\(\sum_{n=1}^{\infty} \frac{1}{n^n} \)

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17

2013 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2013

Taylor series expansion of the function \( f(x) = \frac{x}{1+x} \) around \( x = 0 \) will be

A

\(1 + x + x^2 + x^3 + ... \)

B

\(1 - x + x^2 - x^3 + ... \)

C

\(0 + x + \frac{x^2}{2} + \frac{x^3}{3} + ... \)

D

\(0 + x - x^2 + x^3 - ... \)

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18

2013 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2013

From a 2 m × 1.2 m sheet, squares are cut out from each of the four corners as shown in the figure and then the sides are bent to form an open box. The maximum possible volume (in m³) of the box is __________

Check answer

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19

2013 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2013

A number is as much greater than 75 as it is smaller than 117. The number is:

A

91

B

93

C

89

D

96

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20

2013 · Metallurgical Engineering · Engineering Mathematics · Calculus

Metallurgical Engineering (MT) 2013

The professor ordered to the students to go out of the class.
I                   II                     III                      IV
Which of the above underlined parts of the sentence is grammatically incorrect?

A

I

B

II

C

III

D

IV

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