GATE MA 2017 Paper 1 — page 11

Questions 31–33 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 11 of 22

Let

and

be two sequences in a complete metric space

such that

and

for all

. Then

Your answerChoose one option.

both

and

converge

converges but

need NOT converge

converges but

need NOT converge

neither

nor

converges

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Let

be given by

is rational, and if

is irrational then

, where

is the number of zeroes immediately after the decimal point in the decimal representation of

. Then the Lebesgue integral

equals ________.

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Let

be defined by

Then, at

Your answerChoose one option.

is continuous and the directional derivative of

does NOT exist in some direction

is NOT continuous and the directional derivatives of

exist in all directions

is NOT differentiable and the directional derivatives of

exist in all directions

is differentiable

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2017 · Paper 1