If the function $f(x) = \frac{x}{5} + \frac{5}{x}, (x \neq 0)$ attains its relative maximum value at $x = a$,then $\sqrt{a^2 + 2a - 6} = $

$A$ metal wire $108 \ m$ long is bent to form a rectangle. If the area of the rectangle is maximum,then its dimensions are

In the interval $[-2, 4]$,the absolute maximum of $f(x) = 2x^3 - 3x^2 - 12x + 5$ occurs at $x =$

The maximum and minimum values of ${x^3} - 18{x^2} + 96x$ in the interval $(0, 9)$ are

Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$,then $p^{\prime}(0)$ is

If a cylindrical vessel of given volume $V$ with no lid on the top is to be made from a sheet of metal,then the radius $(r)$ and height $(h)$ of the vessel so that the metal sheet used is minimum,is