EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Application of Derivatives>Assam CEE 2018>Q 1

HARD

Assam CEE

IMPORTANT

Earn 100

The normal to the curve $x = a (\cos θ + θ \sin θ), y = a (\sin θ - θ \cos θ)$ at any point $θ$ is such that

30.77% studentsanswered this correctly

Important Questions on Application of Derivatives

MEDIUM

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Application of Derivatives>Assam CEE 2018>Q 2

y = {x (x - 3)}^{2}

increases for all values of

x

lying in the interval

MEDIUM

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Application of Derivatives>Assam CEE 2017>Q 3

The normal to the curve

2 x^{2} + y^{2} = 12

at the point

(2, 2)

cuts the curve again at:

EASY

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Application of Derivatives>Assam CEE 2017>Q 4

If

f

be a continuous function on

[0, 1]

, differentiable in

(0, 1)

such that

f (1) = 0

, then there exists some

c \in (0, 1)

such that:

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Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Application of Derivatives>Assam CEE 2017>Q 5

Let

g (x) = 2 f (\frac{x}{2}) + f (2 - x)

and

f^{''} (x) < 0 \forall x \in (0, 2) .

Then

g (x)

increases in:

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Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Application of Derivatives>Assam CEE 2016>Q 6

The lengths of the sides of a rectangle of greatest area that can be inscribed in the ellipse

9 x^{2} + 16 y^{2} = 144

are

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Application of Derivatives>Assam CEE 2016>Q 7

Let

f

and

g

be increasing and decreasing functions respectively from

[0, \infty)

to

[0, \infty)

and

h (x) = f \{g (x)\}

. If

h (0) = 0

, then

h (x) - h (1)

is

MEDIUM

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Application of Derivatives>Assam CEE 2016>Q 8

The tangent at

(1, 7)

to the curve

x^{2} = y - 6

touches the circle

x^{2} + y^{2} + 16 x + 12 y + c = 0

at