If $x = p$ and $x = q$ are the points of local maxima and local minima respectively for the function $f(x) = x^5 - 5x^4 + 5x^3 - 10$,then:

The function $f(x) = \int_1^x \{ 2(t - 1)(t - 2)^3 + 3(t - 1)^2(t - 2)^2 \} dt$ is maximum when $x$ is equal to

The cost of running a bus from $A$ to $B$ is $Rs. \left( av + \frac{b}{v} \right)$,where $v \text{ km/h}$ is the average speed of the bus. When the bus travels at $30 \text{ km/h}$,the cost is $Rs. 75$,while at $40 \text{ km/h}$,it is $Rs. 65$. The most economical speed (in $\text{km/h}$) of the bus is:

The perimeter of a sector is a constant. If its area is to be maximum,then the sectorial angle is

If $y = a \log x + bx^2 + x$ has extreme values at $x = -1$ and $x = 2$,then:

At what value of $x$ is the function $f(x) = x(1 - x^2)$ maximum for $0 \leq x \leq 2$?