EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 30 January 2023 Shift 1>Q 144

HARD

JEE Main

IMPORTANT

Earn 100

The number of points on the curve $y = 54 x^{5} - 135 x^{4} - 70 x^{3} + 180 x^{2} + 210 x$ at which the normal lines are parallel to $x + 90 y + 2 = 0$ is:

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Important Questions on Application of Derivatives

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 30 January 2023 Shift 2>Q 145

If the functions

f (x) = \frac{x^{3}}{3} + 2 b x + \frac{a x^{2}}{2}

and

g (x) = \frac{x^{3}}{3} + a x + b x^{2}, a \neq 2 b

have a common extreme point, then

a + 2 b + 7

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 30 January 2023 Shift 2>Q 146

The range of the function

f (x) = \sqrt{3 - x} + \sqrt{2 + x}

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 31 January 2023 Shift 1>Q 147

A wire of length

20 m

is to be cut into two pieces. A piece of length

ℓ_{1}

is bent to make a square of area

A_{1}

and the other piece of length

ℓ_{2}

is made into a circle of area

A_{2}

. If

2 A_{1} + 3 A_{2}

is minimum then

(π ℓ_{1}) : ℓ_{2}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 31 January 2023 Shift 2>Q 148

Let

a_{1}, a_{2}, a_{3}, \dots \dots

. be an A.P. If

a_{7} = 3

, the product

(a_{1} a_{4})

is minimum and the sum of its first

n

terms is zero then

n! - 4 a_{n (n + 2)}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 31 January 2023 Shift 2>Q 149

The absolute minimum value, of the function

f (x) = |x^{2} - x + 1| + [x^{2} - x + 1]

, where

[t]

denotes the greatest integer function, in the interval

[- 1, 2]

, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 31 January 2023 Shift 2>Q 150

Let

f : R - \{2, 6\} \to R

be real valued function defined as

f (x) = \frac{x + 2 x + 1}{x^{2} - 8 x + 12}

. Then range of

f

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 1 February 2023 Shift 1>Q 151

Let

f (x) = 2 x + \tan^{- 1} x

and

g (x) = \log_{e} (\sqrt{1 + x^{2}} + x), x \in [0, 3]

. Then

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 1 February 2023 Shift 1>Q 152

The area enclosed by the closed curve

C

given by the differential equation

\frac{d y}{d x} + \frac{x + a}{y - 2} = 0, y (1) = 0

is

4 π

. Let

P

and

Q

be the points of intersection of the curve

C

and the

y

-axis. If normals at

P

and

Q

on the curve

C

intersect

x

-axis at points

R

and

S

respectively, then the length of the line segment

R S

is