GATE MA year:2025 PYQs & Answers — Page 7

Questions 61–65 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 7 of 7

Consider the inner product space of all real-valued continuous functions defined on

with the inner product

. If

is orthogonal to all the polynomials having degree less than or equal to

, with respect to this inner product, then

is equal to _____ (in integer)

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For

, consider the quadratic form:

Let

be the symmetric matrix associated with the quadratic form

with respect to the standard basis of

. Let

be a non-zero vector, and let

where

is the

identity matrix. Then, the value of

is _____ (in integer)

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Let

be distinct non-zero real numbers, and let

be a polynomial of degree less than 5. If the function

satisfies Morera’s theorem in

, then the value of

is equal to _____ (in integer)

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Let

be a group with identity element

, and let

be such that the following hold:

(i)

(ii)

, and

Then, the least positive integer

for which

is _____ (in integer)

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Let

and

be two metric spaces with

and

If the open ball centred at

with radius

is equal to the open ball centred at

with radius

, then the value of

is _____ (in integer)

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GATE MA year:2025 PYQs

Question 61

Question 62

Question 63

Question 64

Question 65