GATE MA 2023 Paper 1 — page 13

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

Let

. For a sequence

, define

. Let

and

be defined by

Then

Your answerChoose one option.

is a compact linear map and

is NOT a compact linear map

is NOT a compact linear map and

is a compact linear map

both

and

are compact linear maps

NEITHER

NOR

is a compact linear map

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Let

. For

, let

. Define

for all

. Then

Your answerChoose one option.

is continuous but

is NOT continuous

is NOT continuous but

is continuous

both

and

are continuous

NEITHER

NOR

is continuous

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Consider the Cauchy problem

on the initial curve

. Consider the following statements:

: If

, then there exists a unique solution to the Cauchy problem in a neighborhood of

: If

, then there exist infinitely many solutions to the Cauchy problem in a neighborhood of

Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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2023 · Paper 1

Question 37

Question 38

Question 39