GATE MA topic:mathematical-sciences PYQs & Answers — Page 17

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Questions 161–170 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 17 of 65

The number of group homomorphisms from

is equal to ______ (answer in integer)

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Let

and

be a positive real number. For any twice-differentiable function

, let

be the interpolating polynomial of degree at most two that interpolates

at the points

. Define

to be the largest integer such that any polynomial

of degree

satisfies

The value of

is equal to ______ (answer in integer)

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Let

be the interpolating polynomial of degree at most two that interpolates the function

at the points

. Then

(round off to TWO decimal places)

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The maximum of the function

subject to the constraints

is equal to ______ (round off to TWO decimal places)

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If the outward flux of

through the unit sphere

, then

is equal to ______ (round off to TWO decimal places)

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Let

and

. Then

is equal to

Your answerChoose one option.

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Let

. For which one of the following functions

does there exist a sequence of polynomials in

that uniformly converges to

Your answerChoose one option.

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Let

be a function. Which one of the following is a sufficient condition for

to be Lebesgue measurable?

Your answerChoose one option.

is a Lebesgue measurable function

There exist continuous functions

such that

is continuous almost everywhere on

For each

, the set

is Lebesgue measurable

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Let

be given by

. Let

be the

zero matrix. The space

may be identified with

in the usual manner. Which one of the following is correct?

Your answerChoose one option.

is a point of local minimum of

is a point of local maximum of

is a saddle point of

is not a critical point of

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Consider the following statements.

I. There exists a proper subgroup

such that

is a finite group.

II. There exists a subgroup

such that

is isomorphic to

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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GATE MA topic:mathematical-sciences PYQs

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