If a ball is thrown vertically upwards and the height $s$ reached in time $t$ is given by $s = 22t - 11t^{2}$, then the total distance travelled by the ball is (in $\text{ units}$)

$A$ 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

Find two positive numbers $x$ and $y$ such that $x+y=60$ and $x y^{3}$ is maximum.

$A$ particle moving in a straight line starts from rest and the acceleration at any time $t$ is $a - kt^2$, where $a$ and $k$ are positive constants. The maximum velocity attained by the particle is

If $4+3x-7x^2$ attains its maximum value $M$ at $x=\alpha$ and $5x^2-2x+1$ attains its minimum value $m$ at $x=\beta$, then $\frac{28(M-\alpha)}{5(m+\beta)}=$

The minimum value of $\left( x^2 + \frac{250}{x} \right)$ is