If $y=a \log x+b x^2+x$ has its extremum values at $x=-1$ and $x=2$, then

The set of all points, for which $f(x)=x^2 e^{-x}$ strictly increases, is

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