GATE MA topic:mathematics PYQs & Answers — Page 38

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Questions 371–380 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 38 of 65

Let

be given by

for

. Consider the following statements: P:

is equicontinuous on

. Q:

does NOT converge uniformly 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 given by

Consider the following statements: P:

is continuous at

but

is NOT differentiable at

. Q: The directional derivative

exists in the direction of every unit vector

. 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 the solid region in

bounded by the paraboloid

and the plane

. Then the value of

Your answerChoose one option.

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Let

be given by

. Then

has

Your answerChoose one option.

a point of local maximum and a saddle point

a point of local minimum and a saddle point

a point of local maximum and a point of local minimum

two saddle points

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The equation

can be solved in a neighborhood of the point

for some continuously differentiable function

. Then

Your answerChoose one option.

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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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GATE MA topic:mathematics PYQs

Question 36

Question 37

Question 38

Question 39

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Question 45