The volume of a sphere is increasing at the rate of $4 \pi \mathrm{cc} / \mathrm{sec}$. When its volume is $288 \pi \mathrm{cc}$, the rate of increase (in $\mathrm{cm} / \mathrm{sec}$ ) in its radius is

Assertion (A) The function $f(x)=x-\log \left(\frac{1+x}{x}\right), x>0$ has no maximum.

Reason (R) If a function $f(x)$ is strictly increasing in an interval $(a, b)$, then at any point in $(a, b) f^{\prime}(x) \neq 0$

The correct option among the following is

If the tangent and normal drawn to the curve $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$ at $P\left(\theta=\frac{\pi}{2}\right)$ cuts the $X$-axis at $A$ and $B$ respectively, then the area (in sq. units) of $\triangle P A B$ is

$x_1, x_2 \in \mathbf{N}$. If a line having slope 2 is a tangent to the curve $y=x^4-6 x^3+13 x^2-10 x+5$ at points $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right)$, then $x_1 x_2+y_1 y_2=$