Calculus - Engineering Mathematics - Biotechnology Previous Year Questions

1

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

If \(u = \log (e^x + e^y)\), then \(\frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} =\)

A

\(e^x + e^y\)

B

\(e^x - e^y\)

C

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

D

1

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2

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

Evaluate \(\lim_{x\to\infty} x\tan\frac{1}{x}\)

A

\(\infty\)

B

1

C

0

D

-1

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3

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

The Laplace transform of \(f(t) = 2t + 6\) is

A

\(\frac{1}{s} + \frac{2}{s^2}\)

B

\(\frac{3}{s} - \frac{6}{s^2}\)

C

\(\frac{6}{s} + \frac{2}{s^2}\)

D

\(-\frac{6}{s} + \frac{2}{s^2}\)

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4

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

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

A

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

B

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

C

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

D

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

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5

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

The Headmaster ________ to speak to you.
Which of the following options is incorrect to complete the above sentence?

A

is wanting

B

wants

C

want

D

was wanting

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6

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

Velocity of an object fired directly in upward direction is given by \( V = 80 - 32 t \), where \( t \) (time) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?

A

(1, 3/2)

B

(1/2, 1)

C

(1/2, 3/2)

D

(1, 3)

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7

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

If \( |-2X + 9| = 3 \) then the possible value of \( |-X| - X^2 \) would be:

A

30

B

-30

C

-42

D

42

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8

2014 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2014

The limit of the function \( e^{-2t} \sin(t) \) as \( t \to \infty \), is ____

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9

2014 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2014

If \(y = x^x\), then \(\frac{dy}{dx}\) is

A

\(x^x (x-1)\)

B

\(x^{x-1}\)

C

\(x^x (1+\log x)\)

D

\(e^x (1+\log x)\)

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10

2014 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2014

Which of the following statements is true for the series given below?
\[s_n = 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{4}} + \cdots + \frac{1}{\sqrt{n}}\]

A

\(s_n\) converges to \(\log(\sqrt{n})\)

B

\(s_n\) converges to \(\sqrt{n}\)

C

\(s_n\) converges to \(\exp(\sqrt{n})\)

D

\(s_n\) diverges

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11

2014 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2014

The graph of the function \(F(x) = \frac{x}{k_1 x^2 + k_2 x + 1}\) for \(0 < x < \infty\) is

A

Graph A

B

Graph B

C

Graph C

D

Graph D

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12

2015 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2015

Choose the word most similar in meaning to the given word:
Educe

A

Exert

B

Educate

C

Extract

D

Extend

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13

2015 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2015

Operators □, ◇ and → are defined by: a □ b = \(\frac{a-b}{a+b}\) ; a ◇ b = \(\frac{a+b}{a-b}\) ; a→b = ab.
Find the value of (66 □ 6) → (66 ◇ 6).

A

-2

B

-1

C

1

D

2

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14

2016 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2016

The Laplace transform F(s) of the function f(t) = cos (at), where a is constant, is ______ .

A

\(\frac{s^2}{s^2+a^2}\)

B

\(\frac{a}{s^2+a^2}\)

C

\(\frac{s}{s^2+a^2}\)

D

\(\frac{s}{s^2-a^2}\)

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15

2016 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2016

The value of the integral \(\int_{0}^{0.9} \frac{dx}{(1-x)(2-x)}\) is ______ .

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16

2016 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2016

Consider the equation
\[ V = \frac{aS}{b + S + \frac{S^2}{c}} \]
Given \(a = 4\), \(b = 1\) and \(c = 9\), the positive value of \(S\) at which \(V\) is maximum, will be ______.

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17

2017 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2017

The surface area (in m²) of the largest sphere that can fit into a hollow cube with edges of length 1 meter is ______.
Given data: π = 3.14

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18

2017 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2017

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

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19

2017 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2017

The angle (in degrees) between the vectors x = i - j + 2k and y = 2i - j - 1.5k is ______.

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20

2017 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2017

Consider an infinite number of cylinders. The first cylinder has a radius of 1 meter and height of 1 meter. The second one has a radius of 0.5 meter and height of 0.5 meter. Every subsequent cylinder has half the radius and half the height of the preceding cylinder. The sum of the volumes (in cubic meters) of these infinite number of cylinders is _______.
Given data: \( \pi = 3.14 \).

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