GATE MA 2022 Paper 1 — page 13

Questions 37–39 of 65. Imported answers require review unless explicitly marked reviewed.

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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2022 · Paper 1