EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2019>Q 2

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A point is in motion along a hyperbola $y = \frac{10}{x}$ so that its abscissa $x$ increases uniformly at a rate of $1$ unit per second. Then, the rate of change of its ordinate when the point passes through $(5, 2)$

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Important Questions on Application of Derivatives

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2018>Q 3

A ladder

20 ft

long leans against a vertical wall. The top end slides downwards at the rate of

2 ft

per second. The rate at which the lower end moves on a horizontal floor when it is

12 ft

from the wall is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2018>Q 4

A particle is in motion along a curve

12 y = x^{3}

. The rate of change of its ordinate exceeds that of abscissa in

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2020>Q 5

If the tangent to the curve

y^{2} = x^{3}

at

(m^{2}, m^{3})

is also a normal to the curve at

(M^{2}, M^{3}),

then the value of

m M

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2020>Q 6

Consider the curve

y = b e^{- x / a}

, where

a

and

b

are non-zero real numbers. Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2020>Q 7

Tangent is drawn at any point

P (x, y)

on a curve, which passes through

(1, 1)

. The tangent cuts

x

-axis and

y

-axis at

A

and

B

respectively. If

A P : B P = 3 : 1

, then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2018>Q 8

The normal to the curve

y = x^{2} - x + 1,

drawn at the points with the abscissa

x_{1} = 0, x_{2} = - 1

and

x_{3} = 5 / 2

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2020>Q 9

Let

ϕ (x) = f (x) + f (1 - x)

and

f^{"} (x) < 0

in

[0, 1],

then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2020>Q 10

In open interval

(0, \frac{π}{2})