The altitude of a cone is $$20 \mathrm{~cm}$$ and its semi vertical angle is $$30^{\circ}$$. If the semi vertical angle is increasing at the rate of $$2^0$$ per second, then the radius of the base is increasing at the rate of

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

If the tangent to the curve $$xy + ax + by = 0$$ at (1, 1) is inclined at an angle $${\tan ^{ - 1}}2$$ with X-axis, then

Let $$f(x) = a - {(x - 3)^{8/9}}$$, then maxima of $$f(x)$$ is