GATE MA 2019 Paper 1 — page 14

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

Paper practice 65 questionsPage 14 of 22

Let

be non-zero and analytic at all points in

. If

for

, then the residue of

is _____.

(

is the set of all complex numbers,

is the set of all integers and

denotes the set of all complex numbers excluding integers)

Your answerChoose one option.

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The general integral of the partial differential equation

is given by

, where

is a continuously differentiable function.

(

is the set of all real numbers and

)

Then which one of the following is TRUE?

Your answerChoose one option.

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Consider the following statements:

I. If

denotes the additive group of rational numbers and

is a non-trivial homomorphism, then

is an isomorphism.

II. Any quotient group of a cyclic group is cyclic.

III. If every subgroup of a group

is a normal subgroup, then

is abelian.

IV. Every group of order 33 is cyclic.

Which of the above statements are TRUE?

Your answerChoose one option.

II and IV only

II and III only

I, II and IV only

I, III and IV only

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2019 · Paper 1