The set of value$(s)$ of $a$ for which the function $f(x) = \frac{a x^3}{3} + (a + 2) x^2 + (a - 1) x + 2$ possesses a negative point of inflection.

The maximum value of the function $f(x)=3x^3-18x^2+27x-40$ on the set $S=\{x \in R : x^2+30 \leq 11x\}$ is

The maximum area of a triangle whose one vertex is at $(0,0)$ and the other two vertices lie on the curve $y = -2x^2 + 54$ at points $(x, y)$ and $(-x, y)$ where $y > 0$ is:

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 $u =$ ......... $cm/sec$.

The difference between the greatest and the least values of the function $f(x) = \sin(2x) - x$ on the interval $\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]$ is:

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