If the rate of increase of the surface area of a spherical balloon is $5 \text{ cm}^2/\text{sec}$ and the rate of increase of its volume is $10 \text{ cm}^3/\text{sec}$, then the radius of the balloon at that instant is... (in $\text{ cm}$)

If the displacement, velocity, and acceleration of a particle at time $t$ are $x, v$, and $f$ respectively, then which of the following is true?

Two particles $A$ and $B$ move from rest along a straight line with constant accelerations $f$ and $f'$ respectively. If $A$ takes $m$ seconds more than that of $B$ and describes $n$ units more than that of $B$ in acquiring the same velocity, then:

The radius of a circle is increasing at a rate of $0.1 \text{ cm s}^{-1}$. Then the rate of change of area,when its radius is $5 \text{ cm}$,is .........

$A$ ladder of length $13 \ m$ has one end resting against a vertical wall and the other on the ground. If the lower end moves away from the wall at a speed of $2 \ m/min$, then the speed (in $m/min$) at which the upper end falls when the bottom is $5 \ m$ away from the wall is

If the distance $s$ traveled by a particle in time $t$ is $s = a \sin t + b \cos 2t$,then the acceleration at $t = 0$ is