EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2015>Q 95

HARD

JEE Main

IMPORTANT

Earn 100

The distance from the origin, of the normal to the curve, $x = 2 \cos t + 2 t \sin t, y = 2 \sin t - 2 t \cos t a t t = \frac{π}{4},$ is :

100% studentsanswered this correctly

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 - 11th April 2015>Q 96

From the top of a

64

metres high tower, a stone is thrown upwards vertically with the velocity of

48 m / s .

The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration

g = 32 m / s^{2}

, is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 11th April 2015>Q 97

The equation of a normal to the curve,

\sin y = x \sin (\frac{π}{3} + y) at x = 0,

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 11th April 2015>Q 98

Let

k

and

K

be the minimum and the maximum values of the function

f (x) = \frac{{(1 + x)}^{0.6}}{1 + x^{0.6}} in [0, 1]

, respectively, then the ordered pair

(k, K)

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 19th April 2014>Q 99

If the volume of a spherical ball is increasing at the rate of

4 π cc / \sec

then the rate of increase of its radius

(in cm / \sec),

when the volume is

288 π cc

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 19th April 2014>Q 100

If non-zero real numbers

b

and

c

are such that

m i n f (x) > m a x g (x)

, where

f (x) = x^{2} + 2 b x + 2 c^{2}

and

g (x) = - x^{2} - 2 c x + b^{2}, (x \in R)

; then

|\frac{c}{b}|

lies in the interval

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th April 2014>Q 101

If

f (x) = {(\frac{3}{5})}^{x} + {(\frac{4}{5})}^{x} - 1, x \in R,

then the equation

f (x) = 0

has :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 6th April 2014>Q 102

If

x = - 1

and

x = 2

are extreme points of

f (x) = α \log |x| + β x^{2} + x

, then

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 24 June 2022 Shift 1>Q 103

For the function

f (x) = 4 \log_{e} (x - 1) - 2 x^{2} + 4 x + 5, x > 1

, which one of the following is NOT correct?