GATE MA format:mcq PYQs & Answers — Page 16

Questions 151–160 of 366. Imported answers require independent review unless marked reviewed.

Topic practice 366 questionsPage 16 of 37

The real sequence generated by the iterate scheme

Your answerChoose one option.

converges to

, for all

converges to

, whenever

converges to

, whenever

diverges for any

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The initial value problem

where

is a real constant, has

Your answerChoose one option.

a unique solution

exactly two solutions

infinitely many solutions

no solution

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If eigenfunctions corresponding to distinct eigenvalues

of the Sturm-Liouville problem

are orthogonal with respect to the weight function

, then

Your answerChoose one option.

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The steady state solution for the heat equation

with the initial condition

and the boundary conditions

and

, at

Your answerChoose one option.

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Consider

, where

is the subspace topology induced by the Euclidean topology on

, and let

be any topology on

. Consider the following statements:

P: If

is a proper subset of

, then

is not compact. Q: If

is a proper subset of

, then

is not Hausdorff.

Then

Your answerChoose one option.

P is TRUE and Q is FALSE

Both P and Q are TRUE

Both P and Q are FALSE

P is FALSE and Q is TRUE

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Let

be the quotient map, arising from the characteristic function on

, where

is the subspace topology induced by the Euclidean topology on

. Which of the following statements is TRUE?

Your answerChoose one option.

is an open map but not a closed map

is a closed map but not an open map

is a closed map as well as an open map

is neither an open map nor a closed map

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Set

for each

. Define

. Endow

with the product topology, where the topology on each

is the Euclidean topology. Consider the set

with the subspace topology induced from

. Which of the following statements is TRUE?

Your answerChoose one option.

is open in

is locally compact

is dense in

is disconnected

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Let

denote the ring of polynomials in

with real coefficients. Then, the quotient ring

Your answerChoose one option.

a field

an integral domain, but not a field

not an integral domain, but has 0 as the only nilpotent element

a ring which contains non-zero nilpotent elements

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Consider the following conditions on two proper non-zero ideals

and

of a non-zero commutative ring

.\n\nP: For any

, there exists a unique

such that

and

.\n\nQ:

\n\nThen, which of the following statements is TRUE?

Your answerChoose one option.

P implies Q but Q does not imply P

Q implies P but P does not imply Q

P implies Q and Q implies P

P does not imply Q and Q does not imply P

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Let

be a continuous function such that

for some

satisfying

. Define

, for

. Then, which of the following statements is TRUE?

Your answerChoose one option.

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GATE MA format:mcq PYQs

Question 18

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Question 20

Question 21

Question 22

Question 23

Question 24

Question 36

Question 37

Question 38