GATE MA format:nat PYQs & Answers — Page 15

Questions 141–150 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 15 of 23

Let

(the set of all natural numbers). Then

is equal to _____.

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If the differential equation

is solved using the Euler’s method with step-size

, then

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

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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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GATE MA format:nat PYQs

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23