The minimum value of the expression $7 - 20x + 11x^2$ is (in $/11$)

The minimum distance of a point on the curve $y=x^2-4$ from the origin is

If $f(x) = (\sin^4 x + \cos^4 x)$,$0 < x < \frac{\pi}{2}$,then the function has a minimum value of $ . . . . . . $ at $x = . . . . . . $.

$A$ cylindrical container is to be made from a certain solid material with the following constraints: It has a fixed inner volume of $V \ mm^3$,has a $2 \ mm$ thick solid wall,and is open at the top. The bottom of the container is a solid circular disc of thickness $2 \ mm$ and has a radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is $10 \ mm$,then the value of $\frac{V}{250 \pi}$ is

If $ax + \frac{b}{x} \ge c$ for all positive $x$,where $a, b > 0$,then:

The absolute minimum value of $x^4-x^2-2x+5$ is