GATE DA 2025 Paper 1 — page 18

Questions 52–54 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 18 of 22

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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2025 · Paper 1