The minimum value of the function $f(x) = 2 x^3 - 15 x^2 + 36 x - 48$ on the set $A = \{x \mid x^2 + 20 \le 9 x\}$ is

If the minimum value of $f(x) = \frac{5x^2}{2} + \frac{\alpha}{x^5}$ for $x > 0$ is $14$,then the value of $\alpha$ is equal to:

$x$ and $y$ are two variables such that $x > 0$ and $xy = 1$. Then the minimum value of $x + y$ is

The maximum area of a rectangle that can be inscribed in a circle of radius $2 \text{ unit}$ is (in square unit)

The function $f(x)=2 x^3-9 a x^2+12 a^2 x+1$ $(a>0)$ attains its maximum and minimum at $p$ and $q$ respectively and $p^2=q$. Then,$a=$

The equation of motion of a stone,thrown vertically upwards is $s = ut - 6.3t^2$,where the units of $s$ and $t$ are $cm$ and $sec$. If the stone reaches its maximum height in $3$ $sec$,then $u =$ ......... $cm/sec$.