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

If the line $ax + by + 5 = 0$ is a normal to the curve $xy = 1$ then .....

On the interval $[0, 1]$, the function $f(x) = x^{25}(1 - x)^{75}$ attains its maximum value at the point $x = $....

If $f(x) = \int \dfrac{x}{(x^2 + 4)(x^2 + 9)}\, dx$ and $f(0) = \dfrac{1}{5}\log\left(\dfrac{2}{3}\right)$, then $f(1) = $