If $(\alpha, \beta)$ and $(\gamma, \delta)$ where $\alpha < \gamma$ are the turning points of $f(x) = 2x^3 - 15x^2 + 36x - 8$, then $\alpha - \gamma - \beta + \delta =$

$A$ square piece of tin of side $30\,cm$ is to be made into a box without a top by cutting a square of side $x$ from each corner and folding up the flaps to form a box. If the volume of the box is maximum,then its surface area (in $cm^2$) is equal to $............$.

The function $f(x) = x^5 - 5x^4 + 5x^3 - 10$ has a local maximum at $x =$

Let $\sqrt{3}$ be the radius and $\frac{\pi}{3}$ be the semi-vertical angle of a given cone. Then the height of the right circular cylinder of maximum volume that can be inscribed in the given cone is

Find the maximum and minimum values of $f,$ if any,of the function given by $f(x)=|x|, x \in R.$

Consider the region $R = \{(x, y) : x \leq y \leq 9 - \frac{11}{3} x^2, x \geq 0\}$. The area of the largest rectangle with sides parallel to the coordinate axes and inscribed in $R$ is: