Probability and Statistics - Engineering Mathematics - Textile Engineering & Fibre Science Previous Year Questions

1

2007 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2007

Let x be a continuous random variable. If the probability distribution function f(x) of x is given by
\[ f(x) = \begin{cases} \frac{a}{x^2}, & 150 < x < 250 \\ 0, & \text{elsewhere} \end{cases} \]
The value of the constant a is

A

75

B

175

C

275

D

375

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2

2008 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2008

Consider the following data,
21.0 21.6 19.9 19.6 15.6
The variance of this sample rounded off to third decimal place, is

A

25.309

B

15.109

C

10.209

D

5.509

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3

2008 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2008

Two dice are thrown simultaneously. The probability that the total number of dots is equal to 4 is

A

\(\frac{1}{6} \)

B

\(\frac{1}{12} \)

C

\(\frac{1}{18} \)

D

\(\frac{1}{36} \)

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4

2008 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2008

The distribution function \(P_X(k)\) of a random variable \(X\) with parameter \(\lambda\), satisfies the relation \(P_X(k+1) = \frac{\lambda}{k+1} P_X(k)\), \(k = 0,1,2,3 ...\). If \(P_X(0) = e^{-\lambda}\), the expression obtained for \(P_X(k)\) from above relation is

A

\(P_X(k) = \frac{\lambda^k}{k!} e^{\lambda}\)

B

\(P_X(k) = \frac{\lambda^{k+1}}{(k+1)!} e^{\lambda}\)

C

\(P_X(k) = \frac{\lambda^k}{k!} e^{-\lambda}\)

D

\(P_X(k) = \frac{\lambda^{k+1}}{(k+1)!} e^{-\lambda}\)

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5

2009 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2009

Probability of getting 16 in one throw with 3 dice is

A

\(\frac{1}{8}\)

B

\(\frac{3}{16}\)

C

\(\frac{1}{36}\)

D

\(\frac{1}{108}\)

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6

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

If X and Y are two independent random variables, then Variance (X-Y) is

A

Variance (X) + Variance (Y)

B

Variance (X) – Variance (Y)

C

Variance (Y) – Variance (X)

D

Variance (XY)

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7

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

A fair coin is tossed 4 times. What is the probability of getting heads 3 times?

A

1/2

B

1/4

C

1/6

D

1/8

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8

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

If the density function of a random variable X is given by \(f(x) = \begin{cases} \frac{x}{2} & 0 < x < 2 \\ 0 & \text{otherwise} \end{cases}\) then the mean value of X will be

A

4/3

B

1/2

C

0

D

1/6

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9

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

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

A

effeminate

B

ghostlike

C

soft

D

short-lived

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10

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.
Erudition : Scholar

A

steadfast : mercurial

B

competence : strict

C

skill : craftsman

D

nurse : doctor

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11

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

Choose the most appropriate word from the options given below to complete the following sentence:
The two child norms with ______ for the violators will have significant implications for our demographic profile.

A

disincentives

B

incitements

C

restrictions

D

restraints

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12

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

Choose the most appropriate word from the options given below to complete the following sentence:
There is no fixed relation between food and famine; famines can occur with or without substantial ______ in food output.

A

aberration

B

weakening

C

decline

D

deterioration

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13

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

It has taken fifty six long and frustrating years to turn bronze into gold for India's Olympics aspirations. Beijing 2008 marks a defining moment in India's Olympic history. From Delhi to Beijing is a long journey but one that our Olympians have undertaken with courage.
Which of the following statements best sums up the meaning of the above passage:

A

India's participation in Olympics has been frustrating.

B

Beijing Olympics was a landmark in India's Olympic history.

C

Our Olympians have undertaken a long journey to Beijing.

D

India's bronze medal turned into gold at Beijing.

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14

2010 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2010

A gathering of 50 linguists discovered that 4 knew Kannada, Telugu and Tamil, 7 knew only Telugu and Tamil, 5 knew only Kannada and Tamil, 6 knew only Telugu and Kannada. If the number of linguists who knew Tamil is 24 and those who knew Kannada is also 24, how many linguists knew only Telugu?

A

9

B

10

C

11

D

8

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15

2011 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2011

Probability of occurrence of two events E1 and E2 is 0.25 and 0.5, respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither E1 nor E2 occurs is

A

0.11

B

0.25

C

0.39

D

0.86

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16

2011 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2011

A garment factory manufactures shirts. From the past history, it is known that 8 out of 100 collars and 5 out of 100 sleeves are defective. The probability that the assembled shirt will NOT have either of these defects is ______________________

Check answer

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17

2011 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2011

Choose the most appropriate word or phrase from the options given below to complete the following sentence.
The environmentalists hope ______ the lake to its pristine condition.

A

in restoring

B

in the restoration of

C

to restore

D

restoring

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18

2011 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2011

Choose the word from the options given below that is most nearly opposite in meaning to the given word:
Polemical

A

imitative

B

conciliatory

C

truthful

D

ideological

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19

2011 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2011

Choose the most appropriate word from the options given below to complete the following sentence.
Despite the mixture's ______ nature, we found that by lowering its temperature in the laboratory we could dramatically reduce its tendency to vaporize.

A

acerbic

B

resilient

C

volatile

D

heterogeneous

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20

2011 · Textile Engineering & Fibre Science · Engineering Mathematics · Probability and Statistics

Textile Engineering & Fibre Science (TF) 2011

If m students require a total of m pages of stationery in m days, then 100 students will require 100 pages of stationery in

A

100 days

B

m/100 days

C

100/m days

D

m days

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