GATE MA 2017 Paper 1 — page 13

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

Paper practice 65 questionsPage 13 of 22

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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2017 · Paper 1