GATE MA 2019 Paper 1 — page 10

Questions 28–30 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 10 of 22

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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2019 · Paper 1