If $f^{"}\left(x\right)<0, \forall x\in \left(a,b\right)$, then $f^{\text{'}}\left(x\right)=0$

Important Questions on Applications of Derivatives

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Work Book Exercise 7.1>Q 1

A balloon is pumped at $a {\mathrm{cm}}^3/\mathrm{minute}$ the rate  The rate of increase of its surface area when the radius is $b \mathrm{cm},$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Work Book Exercise 7.1>Q 2

$x$ and $y$ are the sides of two squares such that $y=x-x^2$. The rate of change of the area of the second square with respect to that of the first square is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Work Book Exercise 7.1>Q 3

On the curve $x^3=12y$, the abscissa changes at a faster rate than the ordinate. Then, $x$ belongs to the interval

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Work Book Exercise 7.1>Q 4

Two cyclists start from the junction of two perpendicular roads, their velocities being $3v \mathrm{m}/\min$ and $4v \mathrm{m}/\min$. The rate at which the two cyclists are separating is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Work Book Exercise 7.1>Q 5

Moving along the $X$-axis, there are two points with $x=10+6t, x=3+t^2$. The speed with which they are reaching from each other at the time of encounter is ($x$ is in centimetre and $t$ is in second)

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Work Book Exercise 7.1>Q 6

The position of a point in time $t$ is given by $x=a+bt-c{t}^2, y=at+b{t}^2$. Its acceleration at time $t$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Work Book Exercise 7.1>Q 7

Gas is being pumped into a spherical balloon at the rate of $30 {\mathrm{ft}}^3/\min$. Then, the rate at which the radius increases when it reaches the value $15 \mathrm{ft}$, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 7 - Applications of Derivatives>Work Book Exercise 7.1>Q 8

Water is dripping out from a conical funnel of semi-vertical angle $\frac{\pi }{4}$ at the uniform rate of $2 {\mathrm{cm}}^3/\mathrm{s}$ in the surface area, through a tiny hole at the vertex of the bottom. When the slant height of cone is $4 \mathrm{cm}$, find the rate of decrease of the slant height of water, is