GATE MA purpose:exam-prep PYQs & Answers — Page 25

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Questions 241–250 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 25 of 65

Consider the rings

where

denotes the ideal generated by

and

denotes the ideal generated by

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

Every prime ideal of

is a maximal ideal

has exactly one maximal ideal

Every element of

is either nilpotent or a unit

There exists an element in

which is NEITHER nilpotent NOR a unit

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Consider the sequence of Lebesgue measurable functions

given by

For a measurable subset

, denote

to be the Lebesgue measure of

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

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Define the characteristic function

of a subset

For

, let

Let

be defined by

Consider the following two statements:

for every

Then

Your answerSelect all correct options. You can choose more than one.

is TRUE

is FALSE

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Let

, be two functions satisfying the following system of differential equations:

and

, where

are real numbers.

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

, then

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For

, and

, let

be a three-point formula to approximate

for any differentiable function

and

for every polynomial

of degree less than or equal to 2 and for all

, then

Your answerSelect all correct options. You can choose more than one.

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Let

be a twice continuously differentiable function on

such that

and

for all

. Let

for some

. The Newton-Raphson method to compute

is given by

for an initial guess

for some

, then which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

For every

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Let

be defined by

Then

Your answerSelect all correct options. You can choose more than one.

the directional derivative of

in the direction of

the directional derivative of

in the direction of

the directional derivative of

in the direction of

is NOT differentiable at

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Let

and

For each

, define

for all

Let

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

is totally bounded in

is bounded in

is closed in

is open in

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Let

be an abelian group and

be a surjective group homomorphism. Let

for some

. Consider the following statements:

: For every

, there exists an

such that

: Let

be the identity of

and

be the subgroup generated by

. Then

and

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

is TRUE

is FALSE

is TRUE

is FALSE

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Let

be the curve of intersection of the cylinder

and the plane

. Suppose

is oriented in the counterclockwise direction and the

-axis, when viewed from above. If

then the value of

equals __________.

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GATE MA purpose:exam-prep PYQs

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