The function, $f(x)=(3 x-7) x^{2 / 3}, x \in R$ is increasing for all $x$ lying in

The minimum value of $(u-v)^2+\left(\sqrt{2-u^2}-\frac{9}{v}\right)^2$, where $0 < u < \sqrt{2}$ and $v > 0$

The length of three sides of a trapezium are equal, each being 10 cms . Then, the maximum area $\left(\mathrm{cm}^2\right)$ of the trapezium is

Difference between the maximum and minimum values of $f(x)=-\sin ^3 x+3 \sin ^2 x+5$ in $x \in\left[0, \frac{\pi}{2}\right]$ is