The normal to the curve $x=9(1+\cos \theta)$, $y=9 \sin \theta$ at $\theta$ always passes through the fixed point

An open tank with a square bottom is to contain 4000 cubic cm . of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

If $x$ is real, then the difference between the greatest and least values of $\frac{x^2-x+1}{x^2+x+1}$ is

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