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

Open complete paper

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

Open complete paper

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

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

Open complete paper

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

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

Open complete paper

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

Open complete paper

6

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

All engineering students should learn mechanics, mathematics and how to do computation.
                 I                                   II                                     III                                     IV
Which of the above underlined parts of the sentence is not appropriate?

A

I

B

II

C

III

D

IV

Open complete paper

7

2013 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2013

Select the pair that best expresses a relationship similar to that expressed in the pair:
water: pipe:

A

cart: road

B

electricity: wire

C

sea: beach

D

music: instrument

Open complete paper

8

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)

Open complete paper

9

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

Open complete paper

10

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

Open complete paper

11

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

Open complete paper

12

2020 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2020

The difference between the sum of the first \(2n\) natural numbers and the sum of the first \(n\) odd natural numbers is _____.

A

\(n^2 - n\)

B

\(n^2 + n\)

C

\(2n^2 - n\)

D

\(2n^2 + n\)

Open complete paper

13

2012 · Biotechnology · Engineering Mathematics · Calculus

Biotechnology (BT) 2012

A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation \(y = 2x - 0.1x^2\) where \(y\) is the height of the arch in meters. The maximum possible height of the arch is

A

8 meters

B

10 meters

C

12 meters

D

14 meters

Open complete paper