$A$ kite is $120 \ m$ high and $130 \ m$ of string is out. If the kite is moving away horizontally at the rate of $39 \ m/sec$,then the rate at which the string is being paid out is:

If a circular iron sheet of radius $30 \, cm$ is heated such that its area increases at the uniform rate of $6\pi \, cm^2/hr$,then the rate (in $cm/hr$) at which the radius of the circular sheet increases is

$A$ man of $5 \text{ feet}$ height is walking away from a light fixed at a height of $15 \text{ feet}$ at the rate of $K \text{ miles/hour}$. If the rate of increase of his shadow is $\frac{11}{5} \text{ feet/sec}$,then $K=$ (Take $1 \text{ mile} = 5280 \text{ feet}$)

$OA$ and $OB$ are two roads enclosing an angle of $120^{\circ}$. $X$ and $Y$ start from '$O$' at the same time. $X$ travels along $OA$ with a speed of $4 \text{ km/h}$ and $Y$ travels along $OB$ with a speed of $3 \text{ km/h}$. The rate at which the shortest distance between $X$ and $Y$ is increasing after $1 \text{ h}$ is

$A$ spherical iron ball of radius $10 \ cm$ is coated with a layer of ice of uniform thickness. The ice melts at a rate of $50 \ cm^3/min$. When the thickness of the ice is $5 \ cm$,the rate at which the thickness of the ice decreases is:

If the volume of a spherical balloon is increasing at the rate of $900 \ cm^3/sec$,then find the rate of change of the radius of the balloon at the instant when the radius is $15 \ cm$ (in $cm/sec$).