GATE MA topic:mathematical-sciences PYQs & Answers — Page 30

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Questions 291–300 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 30 of 65

The maximum value of

on the line

is _____.

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If the function

attains its local minimum value at the point

, then the value of

is _____ (round off to TWO decimal places).

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If the ordinary differential equation

has a solution of the form

, where

’s are constants and

, then the value of

is _____.

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The Bessel function

satisfy

. Then, the value of

is _____.

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The partial differential equation

is transformed to

using

and

. Then, the value of

is _____.

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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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P: Suppose that

converges at

and diverges at

. Then

converges.\n\nQ: The interval of convergence of the series

.\n\nWhich of the following statements is TRUE?

Your answerChoose one option.

P is true and Q is true

P is false and Q is false

P is true and Q is false

P is false and Q is true

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Let

. Then, which of the following statements is TRUE?

Your answerChoose one option.

is not equicontinuous on

is uniformly convergent on

is equicontinuous on

is uniformly bounded and has a subsequence converging uniformly on

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GATE MA topic:mathematical-sciences PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40