Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 17

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IMPORTANT

Earn 100

A spherical balloon has a variable diameter $\frac{3}{2} (2 x + 1)$ . The rate of change of its volume with respect to $x$ is

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Important Questions on Application of Derivatives

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 18

An edge of a variable cube is increasing at the rate of

3 cm / s

. Find the rate at which the volume of the cube increasing when the edge is

10 cm

long?

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 19

f (x) = \sin x - k x

is decreasing for all

x \in R

, when

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Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 20

A point on the parabola

y^{2} = 18 x

at which the ordinate increases at twice the rate of the abscissa :

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 21

For a particle, displacement-time relation is

t = \sqrt{x} + 3

. Its displacement when its velocity is zero is:

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 22

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is

{t a n}^{- 1} (\frac{1}{2}) .

Water is poured into it at a constant rate of

5 cubic m / \min .

Then the rate

(

in

m / \min),

at which the level of water is rising at the instant when the depth of water in the tank is

10 m;

is:

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 23

A particle moves along the parabola

y = x^{2}

in the first quadrant in such a way that its

x

-coordinate (measured in meters) increases at a rate of

10 m / \sec .

If the angle of inclination

θ

of the line joining the particle to the origin changes, when

x = 3 m,

at the rate of

k rad/sec.

, then the value of

k

is

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 24

A cylindrical tank of radius

10 m

is being filled with wheat at the rate of

314

cubic meter per hour. Then the depth of the wheat is increasing at the rate of

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 25

Every invertible function is