GATE DA year:2025 PYQs & Answers — Page 6

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

Let

be a twice-differentiable function and suppose its second derivative satisfies

for all

. Which of the following statements is/are ALWAYS correct?

Your answerSelect all correct options. You can choose more than one.

has a local minima

There does not exist

and

, such that

has at most one global minimum

has at most one local minimum

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matrix

with real entries satisfies the property:

, for all

, where

denotes the Euclidean norm. Which of the following statements is/are ALWAYS correct?

Your answerSelect all correct options. You can choose more than one.

must be orthogonal

, where

denotes the identity matrix, is the only solution

The eigenvalues of

are either

has full rank

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Consider designing a linear binary classifier

on the following training data:

Class-1:

, Class-2:

Hard-margin support vector machine (SVM) formulation is solved to obtain

and

. Which of the following options is/are correct?

Your answerSelect all correct options. You can choose more than one.

and

The number of support vectors is 3

The margin is

Training accuracy is 98%

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Consider a coin-toss experiment where the probability of head showing up is

. In the

coin toss, let

if head appears, and

if tail appears. Consider

where

is the total number of independent coin tosses. Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

increases, variance of

decreases

Variance of

does not depend on

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Consider a two-class problem in

with class labels

and

. Let

and

be the means of the two classes. Given test sample

, a classifier calculates the squared Euclidean distance (denoted by

) between

and the means of the two classes and assigns the class label that the sample

is closest to. That is, the classifier computes

and assigns the label

, and

otherwise. Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

The sample

is assigned the label

is a linear function of

, where

and

are functions of

and

is a quadratic polynomial in

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Consider the following two relations, named Customer and Person, in a database:

Person ( aadhaar CHAR(12) PRIMARY KEY, name VARCHAR(32));

Customer ( name VARCHAR(32), email VARCHAR(32) PRIMARY KEY, phone CHAR(10), aadhaar CHAR(12), FOREIGN KEY (aadhaar) REFERENCES Person(aadhaar));

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

aadhaar is a candidate key in the Customer relation

phone can be NULL in the Customer relation

aadhaar is a candidate key in the Person relation

aadhaar can be NULL in the Person relation

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Consider a database relation R with attributes ABCDEFG, and having the following functional dependencies:

A → BCE E → DG BC → A

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

A is the only candidate key of R

A, BC are the candidate keys of R

A, BC, E are the candidate keys of R

Relation R is not in Boyce-Codd Normal Form (BCNF)

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Let

be a simple, unweighted, and undirected graph. A subset of the vertices and edges of

are shown below.

Diagram for Data Science and Artificial Intelligence question 58

It is given that

is a shortest path between

and

;

is a shortest path between

and

;

is a shortest path between

and

. Which of the following is/are NOT the edges of

Your answerSelect all correct options. You can choose more than one.

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Let

be such that

for all

. Then

______ (Answer in integer)

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Let

be a dataset of

observations where each

. It is given that

. The covariance matrix computed from

has eigenvalues

. Let

be the direction of maximum variance with

The value of

(Answer in integer)

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GATE DA year:2025 PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60