A cylindrical tank without a top lid is being manufactured to hold a fixed volume of $125\pi$ cubic cm. The minimum surface area required to construct this tank is ............square cm

A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

The equation of tangent to the curves $x = 1 - 3t^2$ and $y = t - 3t^3$ at the point $(-2, 2)$ is...

If $f(x) = \cos x$, then the value of $\int\dfrac{e^{f(x)}(x\sin^3 x + f(x))}{1 - (f(x))^2}dx = $