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JEE • MATHEMATICS • RATE MEASURE

Rate measure practice · Medium

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 31-37 of 37 questions

31 Medium

31 of 37

Application +4 | -1

For a particle moving in a straight line, if time

t

be regarded as a function of velocity

v

, then the rate of change of the acceleration a is given by

View answer and explanation

Correct option: C

- {a^3}\frac{{{d^2}t}}{{d{v^2}}}

Option C (

- {a^3}\frac{{{d^2}t}}{{d{v^2}}}

) is correct because it represents the rate of change of acceleration with respect to time, derived by treating time as a function of velocity.

32 Medium

32 of 37

Application +4 | -1

The radius of a circular plate is increasing at the rate of 0.01 cm/s when the radius is 12 cm. Then , The rate at which the area increase, is

View answer and explanation

Correct option: A

0.24\;\pi \;

sq cm/s

Option A (

0.24\;\pi \; sq cm/s) is correct because it represents the rate of change of the area calculated using the given rate of change of the radius.

33 Medium

33 of 37

Application +4 | -1

A point on the parabola

{y^2} = 18x

at which the ordinate increases at twice the rate of the abscissa, is

View answer and explanation

Correct option: D

\left( {\frac{9}{8},\frac{9}{{\;2}}} \right)\;

Option D

\left( {\frac{9}{8},\frac{9}{{\;2}}} \right)\;

is correct because it satisfies the given condition where the ordinate increases at twice the rate of the abscissa on the parabola.

34 Medium

34 of 37

Application +4 | -1

If the distance s covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

View answer and explanation

Correct option: D

\propto {s^5}

Option D (

\propto {s^5}

) is correct because the acceleration is proportional to the fifth power of the distance covered, derived from the given relationship between distance and velocity.

35 Medium

35 of 37

Application +4 | -1

y = \frac{{x + c}}{{1 + {x^2}}}

where

c

is a constant, then when

y

is stationary,

xy

is equal to

View answer and explanation

Correct option: A

\frac{1}{2}

The correct answer is

\frac{1}{2}

because it is derived by finding the stationary points of the function and then calculating the value of

xy

at those points.

36 Medium

36 of 37

Application +4 | -1

If the velocity

v

of a particle moving along a straight line and its distance

s

from a fixed point on the line are related by

{\upsilon ^2} = {a^2} + {s^2},

then its acceleration equals

View answer and explanation

Correct option: B

Option B (s) is correct because the acceleration is equal to

s

when

{\upsilon ^2} = {a^2} + {s^2}

37 Medium

37 of 37

Application +4 | -1

The radius and height of a cylinder are equal. If the radius of the sphere is equal to the height of the cylinder, then the ratio of the rates of increase of the volume of the sphere and the volume of the cylinder is

View answer and explanation

Correct option: A

4:3

Option A (4:3) is correct because it represents the ratio of the rates of increase of the volume of the sphere and the volume of the cylinder when their dimensions are related as described.

Revision notes and key takeaways

Review RATE MEASURE in your textbook or class notes, then use this set to check your understanding.

Showing 31-37 of 37 questions

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