Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 14

HARD

JEE Main

IMPORTANT

Earn 100

For the curve $x = 2 a \sin t + a \sin t \cos^{2} t$ ; $y = - a \cos^{3} t$

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Important Questions on Applications of Derivatives

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 15

The curve

y = a x^{3} + b x^{2} + c x

is inclined at

45 °

to

x

-axis at (0,0) but it touches

x

-axis at

(1, 0)

, then:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 1

The length of the sub-tangent to the hyperbola

x^{2} - 4 y^{2} = 4

corresponding to the normal having slope unity is

\frac{1}{\sqrt{k}},

then the value of

k

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 2

Cosine of the acute angle between the curves

y = 3^{x - 1} \log_{e} x

and

y = x^{x} - 1

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 3

Acute angle between two curves

x^{2} + y^{2} = a^{2} \sqrt{2}

and

x^{2} - y^{2} = a^{2}

is:

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 4

The minimum distance between a point on the curve

y = e^{x}

and a point on the curve

y = \log_{e} x

is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 5

Tangents are drawn from origin to the curve

y = \sin x +

\cos x

. Then their points of contact lie on the curve:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 6

If $3 x + 2 y = 1$ is a tangent to $y = f (x)$ at $x = \frac{1}{2}$ . Then

$\lim_{x \to 0} \frac{x (x - 1)}{f (\frac{e^{2 x}}{2}) - f (\frac{e^{- 2 x}}{2})}$ .

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 5 - Applications of Derivatives>DPP>Q 7

The distance of point

P

on the curve

y = x^{\frac{3}{2}}

which is nearest to the point

M (4, 0)

from the origin is