EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 25 June 2022 Shift 2>Q 110

HARD

JEE Main

IMPORTANT

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Water is being filled at the rate of $1 {cm}^{3} \sec^{- 1}$ in a right circular conical vessel (vertex downwards) of height $35 cm$ and diameter $14 cm$ . When the height of the water level is $10 cm$ , the rate (in ${cm}^{2} \sec^{- 1}$ ) at which the wet conical surface area of the vessel increases is

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Important Questions on Application of Derivatives

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 25 June 2022 Shift 2>Q 111

If the angle made by the tangent at the point

(x_{0}, y_{0})

on the curve

x = 12 (t + \sin t \cos t)

,

y = 12 {(1 + \sin t)}^{2}, 0 < t < \frac{π}{2}

, with the positive

x

-axis is

\frac{π}{3}

, then

y_{0}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 25 June 2022 Shift 2>Q 112

If the line

y = 4 + k x, k > 0

, is the tangent to the parabola

y = x - x^{2}

at the point

P

and

V

is the vertex of the parabola, then the slope of the line through

P

and

V

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 25 June 2022 Shift 2>Q 113

Let

f (x) = |(x - 1) (x^{2} - 2 x - 3)| + x - 3, x \in ℝ

. If

m

and

M

are respectively the number of points of local minimum and local maximum of

f

in the interval

(0, 4)

, then

m + M

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 26 June 2022 Shift 2>Q 114

Consider a cuboid of sides

2 x, 4 x

and

5 x

and a closed hemisphere of radius

r

. If the sum of their surface areas is constant

k

, then the ratio

x : r

, for which the sum of their volumes is maximum, is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 26 June 2022 Shift 1>Q 115

The sum of the absolute minimum and the absolute maximum values of the function

f (x) = |3 x - x^{2} + 2| - x

in the interval

[- 1, 2]

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 26 June 2022 Shift 1>Q 116

Let

S

be the set of all the natural numbers, for which the line

\frac{x}{a} + \frac{y}{b} = 2

is a tangent to the curve

{(\frac{x}{a})}^{n} + {(\frac{y}{b})}^{n} = 2

at the point

(a, b), a b \neq 0 .

Then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 26 June 2022 Shift 1>Q 117

Let

f (x) = 2 \cos^{- 1} x + 4 \cot^{- 1} x - 3 x^{2} - 2 x + 10, x \in [- 1, 1]

. If

[a, b]

is the range of the function, then

4 a - b

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 27 June 2022 Shift 1>Q 118

The number of distinct real roots of

x^{4} - 4 x + 1 = 0

is