GATE DA year:2025 PYQs & Answers — Page 4

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year:2025

Questions 31–40 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 4 of 7

There are three boxes containing white balls and black balls.

Box-1 contains 2 black and 1 white balls.

Box-2 contains 1 black and 2 white balls.

Box-3 contains 3 black and 3 white balls.

In a random experiment, one of these boxes is selected, where the probability of choosing Box-1 is

, Box-2 is

, and Box-3 is

. A ball is drawn at random from the selected box. Given that the ball drawn is white, the probability that it is drawn from Box-2 is ________ (Round off to two decimal places)

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____________ (Round off to one decimal place)

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On a relation named Loan of a bank:

loan_number	branch_name	amount
L11	Banjara Hills	9000
L14	Kondapur	5000
L15	SR Nagar	4000
L22	SR Nagar	2500
L23	Balanagar	8000
L25	Kondapur	7000
L19	SR Nagar	6500

the following SQL query is executed.

SELECT L1.loan_number

FROM Loan L1

WHERE L1.amount > (SELECT MAX (L2.amount)

FROM Loan L2

WHERE L2.branch_name = 'SR Nagar');

The number of rows returned by the query is ________ (Answer in integer)

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Given data

of the form

, we fit a model

using linear least-squares regression. The optimal value of

is __________ (Round off to three decimal places)

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The naive Bayes classifier is used to solve a two-class classification problem with class-labels

. Suppose the prior probabilities are

and

. Assuming a discrete feature space with

for a specific feature vector

. The probability of misclassifying

is __________ (Round off to two decimal places)

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Let

, where

is a normal random variable with mean

and variance

. The variance of

Your answerChoose one option.

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Let

be such that

. Which one of the following statements is ALWAYS correct?

Your answerChoose one option.

is invertible

Determinant of

is 0

The sum of the diagonal elements of

is 1

and

have the same rank

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Let

be a set of linearly independent vectors in

. Let the

-th element of matrix

be given by

. Which one of the following statements is correct?

Your answerChoose one option.

is invertible

0 is a singular value of

Determinant of

is 0

for some non-zero

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Consider the cumulative distribution function (CDF) of a random variable

The value of

Your answerChoose one option.

0.625

0.25

0.5

0.5625

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A random variable

is said to be distributed as

, denoted by

, if

for

. Let

, where

be independent and identically distributed random variables with

. The value of

, after approximation through Central Limit Theorem, is given by (Recall that

)

Your answerChoose one option.

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GATE DA year:2025 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40