EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 2 September 2020 Shift 2>Q 39

HARD

JEE Main

IMPORTANT

Earn 100

Let $f : (- 1, \infty) \to R$ be defined by $f (0) = 1$ and $f (x) = \frac{1}{x} \log_{e} (1 + x), x \neq 0$ . Then the function $f$

22.22% studentsanswered this correctly

Important Questions on Application of Derivatives

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 2 September 2020 Shift 2>Q 40

The equation of the normal to the curve

y = {(1 + x)}^{2 y} + \cos^{2} (\sin^{- 1} x)

, at

x = 0

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 3 September 2020 Shift 1>Q 41

The function,

f (x) = (3 x - 7) x^{\frac{2}{3}}, x \in R

, is increasing for all

x

lying in

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 3 September 2020 Shift 2>Q 42

Suppose

f (x)

is a polynomial of degree four having critical points at

- 1, 0, 1

. If

T = \{x \in R | f (x) = f (0)\}

, then the sum of squares of all the elements of

T

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 3 September 2020 Shift 2>Q 43

If the surface area of a cube is increasing at a rate of

3.6 {cm}^{2} / \sec

, retaining its shape; then the rate of change of its volume (in

{cm}^{3} / \sec

), when the length of a side of the cube is

10 cm

, is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 3 September 2020 Shift 2>Q 44

If the tangent to the curve

y = e^{x}

at a point

(c, e^{c})

and the normal to the parabola

y^{2} = 4 x

at the point

(1, 2)

intersect at the same point on the

x -

axis, then the value of

c

is .....

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 4 September 2020 Shift 2>Q 45

The area (in sq. units) of the largest rectangle $A B C D$ whose vertices $A$ and $B$ lie on the $x$ -axis and vertices $C$ and $D$ lie on the parabola, $y = x^{2} - 1$ below the $x$ -axis, is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 5 September 2020 Shift 2>Q 46

If

x = 1

is a critical point of the function

f (x) = (3 x^{2} + a x - 2 - a) e^{x},

then

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 5 September 2020 Shift 2>Q 47

Which of the following points lies on the tangent to the curve

x^{4} e^{y} + 2 \sqrt{y + 1} = 3

at the point

(1, 0)

?