GATE MA year:2017 PYQs & Answers — Page 4

Questions 31–40 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 4 of 7

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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Let

be the region in

bounded by the parabola

and the line

. Then

equals ________.

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Let

and

for

. Consider the following statements: (P):

and

are linearly independent solutions of

. (Q): The Wronskian

for all

. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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Let

and

with

be the roots of the indicial equation of

. Then

equals ________.

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Let

be the group of all permutations of the set

. Then the total number of elements of

that commute with

equals ________.

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Let

be the ring of polynomials over

. Then the total number of maximal ideals in the quotient ring

equals ________.

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Let

be an orthonormal basis of a Hilbert space

. Let

be given by

. For each

, define

. Then

Your answerChoose one option.

but for each

for each

but the sequence

is unbounded

there exist

such that

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Consider the subspace

of the Hilbert space

of all square summable real sequences. For

, define

. Consider the following statements: (P):

is pointwise bounded on

. (Q):

is uniformly bounded on

. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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GATE MA year:2017 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40