GATE MA 2026 Paper 1 — page 14

Questions 40–42 of 65. Imported answers require review unless explicitly marked reviewed.

Let

be the unit impulse function defined by

when

and

. Consider the following initial value problem

with

and

. Which one of the following is TRUE?

Your answerChoose one option.

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Which one of the following statements is TRUE?

Your answerChoose one option.

The set of all

real matrices under usual matrix addition and multiplication is a Unique Factorization Domain.

The set of all real valued functions under usual function addition and multiplication is a Unique Factorization Domain.

The set of all polynomials with coefficients in

under usual polynomial addition and multiplication is a Unique Factorization Domain.

The set of Riemann integrable functions in

under usual function addition and multiplication is a Unique Factorization Domain.

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Let

with the supremum norm. Let

be given by

. Which one of the following is TRUE?

Your answerChoose one option.

is bounded but not one-to-one.

is one-to-one but not bounded.

is bounded and the inverse (from the range of

) exists but not bounded.

is bounded and the inverse (from the range of

) is bounded.

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2026 · Paper 1