In $\Delta ABC$,sides $a$ and $b$ are kept constant such that there is an error $\alpha$ in angle $C$. What is the relative error in the area?

The distance $(s)$ travelled by a particle in time $t$ is given by $s = 4t^2 + 2t + 3$. The velocity of the particle when $t = 3$ seconds is

If $V = \frac{4}{3}\pi r^3$,find the rate of change of $V$ with respect to $t$ when $r = 10$ and $\frac{dr}{dt} = 0.01$.

$A$ horse runs along a circle with a speed of $20 \, km/hr$. $A$ lantern is at the centre of the circle. $A$ fence is along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse moves along the fence at the moment when it covers $1/8$ of the circle is (in $km/hr$):

The rate of change of volume of a sphere with respect to its surface area when the radius is $4 \text{ cm}$ is

The side of an equilateral triangle expands at the rate of $2 \, cm/s$. The rate of increase of its area when each side is $10 \, cm$ is: