Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 11

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

If the ratio of base radius and height of a cone is $1 : 2$ and percentage error in radius is $λ %,$ then the error in its volume is

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Important Questions on Applications of Derivatives

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 12

The pressure

P

and volume

V

of a gas are connected by the relation

P V^{\frac{1}{4}} =

constant. The percentage increase in the pressure corresponding to a definition of

\frac{1}{2} %

in the volume is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 13

The curve

y - e^{x y} + x = 0

has a vertical tangent at the point

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 14

The equation of normal at the point

θ

of the curve

x = a \cos^{3} θ, y = a \sin^{3} θ

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 15

The equation of the tangent to the curve

x = \frac{3 a t}{1 + t^{2}}, y = \frac{3 a t^{2}}{1 + t^{2}}

at the point

t = 2

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 16

If the normal at the point

t_{1}

on the curve

x y = c^{2}

meets the curve again at

t_{2},

then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 17

The tangent to the curve

3 x y^{2} - 2 x^{2} y = 1

at

(1, 1)

meets the curve again at

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 18

The equation of the normal to the curve

y = 1 - 2^{\frac{x}{2}}

at the point of intersection with the

Y

-axis is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Target Exercises>Q 19

The area of the triangle formed by the positive

X

-axis, the tangent and the normal to the circle

x^{2} + y^{2} = 9

at

(2, \sqrt{5})

is