GATE DA year:2025 PYQs & Answers — Page 2

Questions 11–20 of 65. Imported answers require independent review unless marked reviewed.

Suppose

and

are random variables. The conditional expectation of

given

is denoted by

. Then

equals

Your answerChoose one option.

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The number of additions and multiplications involved in performing Gaussian elimination on any

upper triangular matrix is of the order

Your answerChoose one option.

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The sum of the elements in each row of

is 1. If

, which one of the following statements is correct (for

Your answerChoose one option.

The equation

has no solution

The equation

has exactly two solutions

The equation

has infinitely many solutions

The equation

has a unique solution

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Let

. Let

denote the

th derivative of

evaluated at

. What is the value of

? (Note:

denotes factorial)

Your answerChoose one option.

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Let

and

be any two propositions. Consider the following propositional statements.

where

denotes conjunction (AND operation),

denotes disjunction (OR operation), and

denotes negation (NOT operation). Which one of the following options is correct?

(Note:

denotes logical equivalence)

Your answerChoose one option.

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If a relational decomposition is not dependency-preserving, which one of the following relational operators will be executed more frequently in order to maintain the dependencies?

Your answerChoose one option.

Selection

Projection

Join

Set union

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Consider the following three relations:

Car (model, year, serial, color)

Make (maker, model)

Own (owner, serial)

A tuple in Car represents a specific car of a given model, made in a given year, with a serial number and a color. A tuple in Make specifies that a maker company makes cars of a certain model. A tuple in Own specifies that an owner owns the car with a given serial number. Keys are underlined; (owner, serial) together form key for Own. (

denotes natural join)

Which one of the following options describes what the above expression computes?

Your answerChoose one option.

All owners of a red car, a car made by ABC, or a red car made by ABC

All owners of more than one car, where at least one car is red and made by ABC

All owners of a red car made by ABC

All red cars made by ABC

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Consider a hash table of size 10 with indices

, with the hash function

where linear probing is used to handle collisions. The hash table is initially empty and the following sequence of keys is inserted into the hash table: 1, 4, 5, 6, 14, 15. The indices where the keys 14 and 15 are stored are, respectively

Your answerChoose one option.

2 and 5

2 and 6

4 and 5

4 and 6

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Let

be a continuous random variable whose cumulative distribution function (CDF)

, for some

, is given as follows:

If the median of

is 3, then what is the value of

Your answerChoose one option.

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Let

, where

is a standard normal random variable, and

are two unknown constants. It is given that

where

denotes the expectation of random variable

. The values of

are:

Your answerChoose one option.

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GATE DA year:2025 PYQs

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20