GATE MA year:2023 PYQs & Answers — Page 5

Questions 41–50 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 5 of 7

Let

and

be two linearly independent solutions of the ordinary differential equation

Let

be such that

and

for all

. Consider the following statements:

for all

Then

Your answerChoose one option.

is TRUE and

is FALSE

is FALSE and

is TRUE

both

and

are FALSE

both

and

are TRUE

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Let

and

be an analytic function given by the power series

, where

and

for

. Consider the following statements:

: If

, then

is one-one in some neighbourhood of

: If

, then

is a closed subset of

Which of the following statements is/are correct?

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

is TRUE

is FALSE

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Let

be an open connected subset of

containing

. Let

. Consider the following statements:

: There exists

such that

for all

, where

denotes the third derivative of

Then

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

is TRUE

is FALSE

is TRUE

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Let

be a topological space, where the topology

is defined as

Which of the following statements is/are correct?

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

is first countable

is Hausdorff

is separable

The closure of

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Let

, where

denotes the set of rational numbers and

denotes the set of integers. For

, let

denote the ideal generated by

Which of the following statements is/are correct?

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

is an irreducible element in

, then

is a prime ideal in

is a unique factorization domain

is a prime ideal in

is NOT a principal ideal domain

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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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GATE MA year:2023 PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50