GATE MA year:2017 PYQs & Answers — Page 2

Questions 11–20 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 2 of 7

Let

be a non-abelian group of order 125. Then the total number of elements in

equals ______.

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Let

and

be subfields of a finite field

consisting of

and

elements, respectively. Then the total number of elements in

equals ______.

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Consider the normed linear space

equipped with the norm given by

and the subspace

. Let

be the linear functional on

given by

. If

, is a Hahn-Banach extension of

, then

equals ______.

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For

, define

, where

. Then

equals

Your answerChoose one option.

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If the fourth order divided difference of

, at the points 0.1, 0.2, 0.3, 0.4, 0.5 is 5, then

equals ______.

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If the quadrature rule

, where

, is exact for all polynomials of degree

, then

equals ______.

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, where

is a differentiable function, then

satisfies

Your answerChoose one option.

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The partial differential equation

Your answerChoose one option.

hyperbolic along the line

elliptic along the line

parabolic along the line

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Let

and

be topological spaces and let

be a continuous surjective function. Which one of the following statements is TRUE?

Your answerChoose one option.

is separable, then

is separable

is first countable, then

is first countable

is Hausdorff, then

is Hausdorff

is regular, then

is regular

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Consider the topology

. Then, the topological space

Your answerChoose one option.

compact but NOT connected

connected but NOT compact

both compact and connected

neither compact nor connected

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GATE MA year:2017 PYQs

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20