Rate of Change of Quantities

A particle moves along a straight line according to the law $s=\frac{1}{3}{t}^3-3t^2+9t+17,$ where $\text{'}s\text{'}$ is in meter and $\text{'}t\text{'}$ is in second. Its velocity decreases in

Water is running into an underground right circular conical reservoir, which is $10 \mathrm{m}$ deep and radius of its base is $5 \mathrm{m}.$ If the rate of change in the volume of water in the reservoir is $\frac{3}{2}\frac{\pi {\mathrm{m}}^3}{\min }$, then the rate (in $\frac{\mathrm{m}}{\min }$) at which water rises in it, when the water level is $4 \mathrm{m}$, is

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing,is

In which of the following range $x$ lies such that $9x^2-12x-40$ increases more rapidly than $2x^3+7$.

At which point on the parabola $x^2=4y,$ the rate of increase of the $x$- coordinate is the same as the rate of the increase of $y$- coordinate

If there is $2\%$ error in measuring the radius of Sphere, then .......... will be the percentage error in the surface area.

If $y=7x-x^3$ and x increases at the rate of $4$ units per second, then the rate of change in slope of the curve when $x=3$, is

A point on the parabola $y^2=18x$ at which the ordinate increases at twice the rate of the abscissa is:

At which point on the parabola $x^2=4y,$ the rate of increase of the $x$- coordinate is the same as the rate of the increase of $y$- coordinate.

A point on the parabola $y^2=18x$ at which the ordinate increases at twice the rate of the abscissa, is

The distance in$$ meters covered by a body in t seconds, is given by $s=3t^2-8t+5.$

The body will stop after

There are two points moving along the $y-$axis which are given by $y=20+6t, y=13+t^2.$ Find velocity at which they are approaching  each other at the time of encounter (in $\mathrm{cm}/\sec$)

If the rate of change of area of rhombus with respect to it's side is equal to the side of rhombus, then the angles of rhombus are$\dots \dots$

The displacement is $\text{'}s\text{'}$ of the particle at time $\text{'}t\text{'}$ is given by $s=t^3-4t^2-52$. Find its velocity and acceleration at time $t=2s$.

The surface area of a spherical balloon is increasing at the rate of $2 {\mathrm{cm}}^2/\sec$. If the volume of the balloon is increasing at $a {\mathrm{cm}}^3/\sec$, when the radius of the balloon is $6 \mathrm{cm}$, then $a$ is

The approximate value of $\cos 31°$ is (take $1°=0.0174$ )

The $x-$coordinate changes on the curve $y=3x^5+15x-8$ at the rate of $\frac{1}{5}\mathrm{units}/\sec$, $A\left(x_1, y_1\right), B\left(x_2, y_2\right)$ are the points on the curve at which the $y-$coordinate changes at the rate of $6 \mathrm{units}/\sec$, then the slope of $AB=$

The population of a city grows at the annual rate of $3\%$. What percentage increase is expected in $5$ years?