The difference between the absolute maximum and absolute minimum values of the function $f(x)=2x^3-15x^2+36x-30$ on the interval $[-1, 4]$ is:

If the absolute maximum and absolute minimum values of the function $f(x) = x^3 - 2x^2 + x - 3$ defined on $[0, 2]$ are $M$ and $m$ respectively, then $M + m =$

$A$ tank with a rectangular base and rectangular sides,open at the top is to be constructed so that its depth is $4 \ m$ and volume is $36 \ m^3$. If building of the tank costs $₹ 100$ per square meter for the base and $₹ 50$ per square meter for the sides,then the cost of the least expensive tank is:

If the local maximum value of the function $f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^2 x}, \quad x \in\left(0, \frac{\pi}{2}\right)$,is $\frac{k}{e}$,then $\left(\frac{ k }{ e }\right)^8+\frac{ k ^8}{ e ^5}+ k ^8$ is equal to

The maximum value of ${\left( {\frac{1}{x}} \right)^{2{x^2}}}$ is

All the points on the curve $y^{2}=4a|x+a \sin(x/a)|$,where the tangent is parallel to the $x$-axis,lie on: