GATE MA format:nat PYQs & Answers — Page 5

Questions 41–50 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 5 of 23

Let

be the interpolating polynomial of degree at most two that interpolates the function

at the points

. Then

(round off to TWO decimal places)

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The maximum of the function

subject to the constraints

is equal to ______ (round off to TWO decimal places)

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If the outward flux of

through the unit sphere

, then

is equal to ______ (round off to TWO decimal places)

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Let

denote the space of all real-valued Lebesgue square-integrable functions on

, with the usual norm

. Let

be the subspace of

consisting of all the polynomials of degree at most 1. Let

be such that

, and

. Then

(round off to TWO decimal places)

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The maximum value of

subject to the constraints

is equal to

(round off to TWO decimal places)

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Let

be the field extension of

obtained by adding all the roots of the polynomial equation

. The number of distinct fields

such that

is equal to

(answer in integer)

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Let

be the subset of

consisting of all

such that

for all

. The number of elements in

is equal to

(answer in integer)

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Let

be a continuously differentiable path from

and let

be defined by

. The line integral of

along

is equal to

(round off to TWO decimal places)

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Let

be the solution of the initial value problem

, then

is equal to

(round off to TWO decimal places)

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The boundary value problem

has infinitely many distinct solutions when

is equal to

(round off to TWO decimal places)

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GATE MA format:nat PYQs

Question 33

Question 34

Question 35

Question 57

Question 58

Question 59

Question 60

Question 61

Question 62

Question 63