GATE MA 2025 Paper 1 — page 19

Questions 55–57 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 19 of 22

Consider the sequence

of continuous functions on

defined by

Then, which of the following is/are TRUE?

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

The sequence

converges pointwise but not uniformly on

The sequence

converges uniformly on

for all

and

for all

and

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For

, let

. Then, which of the following is/are TRUE?

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

converges uniformly on

converges pointwise but not uniformly on

converges uniformly on every compact subset of

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Let

and

be provided with the respective Euclidean topologies, and let

be assigned the subspace topology induced from

. If

is a non-constant continuous function, then which of the following is/are TRUE?

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

maps closed sets to closed sets

is injective

is surjective

There exists

such that

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2025 · Paper 1