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

A tank with a rectangular base and rectangular sides, open at the top is made. Depth of the tank is $4$ m and its volume is $36$ cubic meters. For making a tank cost of base material used is Rs. $100$ per sq. meter and that of sides is Rs. $50$ per sq. meter. Then minimum cost of tank is ..............

A particle is fired straight up from the ground. Its height in feet after $t$ second is given by $s(t) = 128t - 16t^2$. The velocity of the particle when it hits the ground is...

The value of $c$ satisfied by the Rolle's theorem for the function $f(x) = x^2(1 - x)^2$, $x \in [0, 1]$ is...