The abscissa of the point on the curve $y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{-\frac{x}{a}}\right)$ where the tangent is parallel to the X -axis is

The Number of values of C that satisfy the conclusion of Rolle's theorem in case of following function $\mathrm{f}(x)=\sin 2 \pi x, x \in[-1,1]$ is

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

The function $\mathrm{f}(x)=2 x^3-9 x^2+12 x+2$ is decreasing in