GATE MA purpose:exam-prep PYQs & Answers — Page 49

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Questions 481–490 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 49 of 65

Let

be any polynomial function of degree at most 2 over

(the set of all real numbers). If the constants

and

are such that

then

is equal to _____ (round off to 2 places of decimal).

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Let

denote the value of the line integral

, where

, a circle of radius 2 with centre at origin of the

-plane is traversed once in the anti-clockwise direction. Then

is equal to _____.

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The temperature

at any point

is inversely proportional to the square of the distance of

from the origin. If the value of the temperature

at the point

, then the rate of change of

at the point

in the direction of

is equal to _____ (round off to 2 places of decimal).

(

is the set of all real numbers,

and

denotes

excluding the origin.)

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Let

be a continuous function defined on

such that

for all

. If the area bounded by

and

, where

, then

is equal to _____ (round off to 1 place of decimal).

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If the characteristic polynomial and minimal polynomial of a square matrix

are

and

, respectively, then the rank of the matrix

is _____, where

is the identity matrix of appropriate order.

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Let

be a primitive complex cube root of unity and

. Then the degree of the field extension

over

(the field of rational numbers) is _____.

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Let

Then the greatest integer less than or equal to

is _____.

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Consider the system:

is a basic feasible solution of the above system (where

and

are real constants), then

is equal to _____.

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Let

be a function defined by

. Then the number of zeros of

is _____.

(

is the set of all complex numbers)

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Let

be a normed linear space with the norm

Let

be the bounded linear functional defined by

Then

is equal to _____ (round off to 3 places of decimal).

(

is the set of all complex numbers.)

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