Probability and Statistics - Engineering Mathematics - Naval Architecture & Marine Engineering Previous Year Questions

1

2022 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2022

If a population has exponential distribution with mean 1, then its median is

A

e

B

1

C

\log_e 2

D

\log_e 3

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2

2022 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2022

We have two coins. One is biased with the probability for head being 1.0 and the other is a fair coin. One coin is chosen at random and is tossed twice. If we obtain head both times, then the probability of the chosen coin being a fair coin is ______ (correct to one decimal place).

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3

2023 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2023

“You are delaying the completion of the task. Send ________ contributions at the earliest.”

A

you are

B

your

C

you’re

D

yore

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4

2023 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2023

In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.
When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.
Based only on the above information, which one of the following statements can be logically inferred with certainty?

A

Every Fields medalist has won a medal in an International Mathematics Olympiad.

B

Everyone who has dropped out of college has won the Fields medal.

C

All Fields medalists are part-time poets.

D

Some Fields medalists have dropped out of college.

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5

2023 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2023

Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?
(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.

A

only (i)

B

only (iii) and (iv)

C

only (i) and (ii)

D

(i), (ii) and (iii)

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6

2023 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2023

To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

A

400

B

600

C

800

D

200

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7

2023 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2023

Let \(X\) be any random variable and \(Y = -2X + 3\). If \(E[Y] = 1\) and \(E[Y^2] = 9\), then which of the following are TRUE?

A

\(E[X] = 1\)

B

\(E[X] = -2\)

C

\(Var(X) = 1\)

D

\(Var(X) = 2\)

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8

2024 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2024

If \( X \) is a Poisson random variable with mean \( \mu = 1 \), then the conditional probability of the event \( \{X \geq 2\} \) given that the event \( \{X \geq 4\} \) has occurred, is __________ (rounded off to two decimal places).

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9

2025 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture & Marine Engineering (NM) 2025

A box contains 12 red and 8 blue balls. Two balls are drawn randomly from the box without replacement.
The probability of drawing a pair of balls having the same color is_____
(rounded off to three decimal places).

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10

2026 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2026

Match the distribution with its corresponding probability density/mass function.

Distribution type	Probability density/mass function
(P) Binomial Distribution	(1) \( f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp \left( -\frac{1}{2} \left( \frac{x-\mu}{\sigma} \right)^2 \right) , \sigma > 0 \)
(Q) Poisson Distribution	(2) \( f(x) = \binom{n}{x} p^x (1-p)^{n-x} , \quad x=0,1,2,...,n \)
(R) Normal Distribution	(3) \( f(x) = \frac{\mu^x}{x!} \exp(-\mu) , \quad x=0,1,2,... \)
(S) Exponential Distribution	(4) \( f(x) = \lambda \exp(-\lambda x) , \quad x>0 \)

A

P → 2, Q → 3, R → 1, S → 4

B

P → 1, Q → 3, R → 2, S → 4

C

P → 3, Q → 2, R → 1, S → 4

D

P → 2, Q → 4, R → 3, S → 1

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11

2026 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2026

The borehole data for resource estimation for an iron ore deposit are shown. The average grade of the deposit, in %, is __________. (rounded off to two decimal places)

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12

2026 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2026

Using linear regression (least squares), the best-fit line for the given dataset is \( y = 2.2x + 2.3 \). Given the residual sum of squares is 25.8, the coefficient of determination ( \( r^2 \) ), is __________. (rounded off to two decimal places)

x	2	3	4	5
y	8	9	7	16

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13

2026 · Naval Architecture & Marine Engineering · Engineering Mathematics · Probability and Statistics

Naval Architecture and Marine Engineering (NM) 2026

Consider a case where two identical six-faced fair dice are rolled simultaneously.
The probability of getting even numbers in both AND a sum equal to 5 and above is ______ (rounded off to two decimal places).

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