If $f(x)=x e^{x(1-x)}$, then $f(x)$ is

If $$u=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$$ and $$v=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$, then $$\frac{d u}{d v}$$ is

The distance '$$s$$' in meters travelled by a particle in '$$t$$' seconds is given by $$s=\frac{2 t^3}{3}-18 t+\frac{5}{3}$$. The acceleration when the particle comes to rest is :

A particle moves along the curve $$\frac{x^2}{16}+\frac{y^2}{4}=1$$. When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is