EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 26 Feb 2021 Shift 2>Q 34

HARD

JEE Main

IMPORTANT

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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 - 26 Feb 2021 Shift 2>Q 35

Let

a

be an integer such that all the real roots of the polynomial

2 x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 10 x + 10

lie in the interval

(a, a + 1)

. Then,

| a |

is equal to ______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 2 September 2020 Shift 1>Q 36

If the tangent to the curve

y = x + \sin y

at a point

(a, b)

is parallel to the line joining

(0, \frac{3}{2})

and

(\frac{1}{2}, 2)

, then

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 2 September 2020 Shift 1>Q 37

If

p (x)

be a polynomial of degree three that has a local maximum value

8

at

x = 1

and a local minimum value

4

at

x = 2

then

p (0)

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 2 September 2020 Shift 1>Q 38

Let

P (h, k)

be a point on the curve

y = x^{2} + 7 x + 2

, nearest to the line,

y = 3 x - 3

. Then the equation of the normal to the curve at

P

is

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 39

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

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 :