GATE MA year:2021 PYQs & Answers — Page 6

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

Topic practice 65 questionsPage 6 of 7

Consider the following topologies on the set

of all real numbers.

is the upper limit topology having all sets

as basis.

is the standard topology having all sets

as basis. Then

Your answerChoose one option.

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Let

denote the set of all real numbers. Consider the following topological spaces.

, where

is the upper limit topology having all sets

as basis.

, where

. Then

Your answerChoose one option.

both

and

are connected

is connected and

is NOT connected

is NOT connected and

is connected

neither

nor

is connected

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Let

be an inner product on the vector space

over

. Consider the following statements: P:

for all

. Q: If

for all

, then

. 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 group of order

with center having

elements. Then the number of conjugacy classes in

is __________.

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Let

be a finite field and

be the group of all nonzero elements of

under multiplication. If

has a subgroup of order 17, then the smallest possible order of the field

is __________.

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Let

and

be the positively oriented boundary of

. Then the value of the integral

is __________.

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Let

and

be the function defined by

for

, then

__________.

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The number of zeroes (counting multiplicity) of

in the annular region

is __________.

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Let

be a square matrix such that

, where

denotes the determinant of a square matrix

. If

, then the geometric multiplicity of the eigenvalue

is __________.

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(

) is the power series solution of the differential equation

, then

__________.

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GATE MA year:2021 PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50