EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2018 Shift 1>Q 2

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A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of $0.02 cm / s$ . The rate of increase of its volume when radius is $10 cm$ is________ $π$ $c m^{3} / s$

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Important Questions on Application of Derivatives

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2017>Q 3

The volume

V

and depth

x

of water in a vessel are connected by the relation

V = 5 x - \frac{x^{2}}{6}

and the volume of water is increasing at the rate of

5 {cm}^{3} / \sec .

When

x = 2 cm

, the rate at which the depth of water is increasing is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2017>Q 4

The angle between a pair of tangents drawn from a point

T

to the circle

x^{2} + y^{2} + 4 x - 6 y + 9 \sin^{2} α + 13 \cos^{2} α = 0

is

2 α .

The equation of the locus of the point

T

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2018 Shift 1>Q 5

The two curves

x^{3} - 3 x y^{2} + 2 = 0

and

3 x^{2} y - y^{3} - 2 = 0

intersect at an angle of

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2019 Shift 1>Q 6

If

f (x) = x^{3} + b x^{2} + c x + d

and

0 < b^{2} < c

, then in

(- \infty, \infty)

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2018 Shift 1>Q 7

The interval in which the function

f (x) = \frac{4 x^{2} + 1}{x}

is strictly decreasing is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2017>Q 8

The function

f (x) = \sin x - k x - c

, where

k

and

c

are constants, decreases always when

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2019 Shift 1>Q 9

A wire

34 cm

long is to be bent in the form of a quadrilateral of which each angle is

90^{°}

. What is the maximum area which can be enclosed inside the quadrilateral?

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Application of Derivatives>VITEEE 2018 Shift 1>Q 10

If at

x = 1,

the function

x^{4} - 62 x^{2} + a x + 9

attains its local maximum value, on the interval

[0, 2]

, then the value of

a

is