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

$$f(x)=\log |\sin x|$$, where $$x \in(0, \pi)$$ is strictly increasing on

The velocity of a particle at time $$t$$ is given by the relation $$v=6 t-\frac{t^2}{6}$$. Its displacement S is zero at $$\mathrm{t}=0$$, then the distance travelled in $$3 \mathrm{~sec}$$ is

The radius of a circular plate is increasing at the rate of $$0.01 \mathrm{~cm} / \mathrm{sec}$$, when the radius is $$12 \mathrm{~cm}$$. Then the rate at which the area increases is