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 $\text{ units}$)

If $f(x)=a \log |x|+b x^2+x$ has extreme values at $x=-1$ and $x=2$,then the ordered pair $(a, b)=$

The maximum value of $\frac{\log _{e} x}{x}$,if $x>0$ is

If the function $f(x) = x^4 - 62x^2 + ax + 9$ is maximum at $x = 1$,then the value of $a$ is

$A$ cone of maximum volume is inscribed in a sphere of radius $R$. The ratio of the height of the cone to the diameter of the sphere is:

$A$ manufacturer can sell $x$ items at a price of rupees $\left(5 - \frac{x}{100}\right)$ each. The cost price of $x$ items is Rs. $\left(\frac{x}{5} + 500\right)$. The number of items that the manufacturer should sell to earn the maximum profit is