The distance 's' in meters covered by a particle in t seconds is given by $$s=2+27 t-t^3$$. The particle will stop after _________ distance.

The curve $$y=a x^3+b x^2+c x+5$$ touches $$X$$-axis at $$P(-2,0)$$ and cuts $$Y$$-axis at a point $$Q$$, where its gradient is 3, then

The minimum value of the function f(x) = x log x is

The maximum area of the rectangle that can be inscribed in a circle of radius $$r$$ is