GATE MA 2020 Paper 1 — page 12

Questions 34–36 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 12 of 22

Let

be the ring of integers modulo 225. If

is the number of prime ideals and

is the number of nontrial units in

, then

is equal to

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Let

be the solution of

, where

is a twice continuously differentiable function. If

, and

, then the value of

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Let

be an orthonormal basis for a separable Hilbert space

with the inner product

. Define

for

. Then

Your answerChoose one option.

the closure of the span

equals

for all

is an orthogonal subset of

there does not exist nonzero

such that

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2020 · Paper 1