GATE MA year:2021 PYQs & Answers — Page 3

Questions 21–30 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 3 of 7

Consider the following statements:

is a metric on

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be a twice continuously differentiable scalar field such that

. Let

be the surface

and

be unit outward normal to

. Then the value of

Your answerChoose one option.

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Consider the following statements: P: Every compact metrizable topological space is separable. Q: Every Hausdorff topology on a finite set is metrizable. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Consider the following topologies on the set

of all real numbers:

. Then the closure of the set

Your answerChoose one option.

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Let

be differentiable. Let

and

be the direction derivatives of

in the directions of the unit vectors

and

, respectively. If

and

, then

_____.

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Let

denote the boundary of the square region

with vertices

and

oriented in the counter-clockwise direction. Then

__________.

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The number of 5-Sylow subgroups in the symmetric group

of degree 5 is _____.

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Let

be the ideal generated by

in the polynomial ring

, where

denotes the ring of integers modulo 3. Then the number of units in the quotient ring

is ______.

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Let

be a linear transformation such that

, and

. Then the rank of

is _____.

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Let

be the solution of the following initial value problem

Then

__________.

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GATE MA year:2021 PYQs

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20