$A$ particle is moving in a straight line according to the equation $s = 45t + 11t^2 - t^3$. The time at which it will come to rest is ......... $sec$.

The volume of a cube is increasing at the rate of $8 \, cm^{3}/s$. How fast is the surface area increasing when the length of an edge is $12 \, cm$?

If the law of motion in a straight line is $s = \frac{1}{2}vt$,then acceleration is

The edge of a cube is increasing at the rate of $5 \, cm/\sec$. How fast is the volume of the cube increasing when the edge is $12 \, cm$ long? (in $cm^3/\sec$)

If the sides of a triangle vary slightly in such a way that its circumradius remains constant,then $\frac{da}{\cos A} + \frac{db}{\cos B} + \frac{dc}{\cos C}$ is equal to

$A$ water tank has the shape of a right circular cone with its axis vertical and vertex downwards. Its semi-vertical angle is $\tan^{-1} \frac{3}{4}$. Water is poured into it at a constant rate of $6 \text{ m}^3/\text{hr}$. The rate (in $\text{m}^2/\text{hr}$) at which the wet curved surface area of the tank is increasing when the depth of water in the tank is $4 \text{ m}$ is: