The function $f(x) = \sin x (1 + \cos x)$ is maximum at $x = \dots$

Let $V_1$ be the volume of a given right circular cone with $O$ as the centre of the base and $A$ as its apex. Let $V_2$ be the maximum volume of the right circular cone inscribed in the given cone whose apex is $O$ and whose base is parallel to the base of the given cone. Then,the ratio $V_2 / V_1$ is

$A$ missile is fired from the ground level and rises $x$ meters vertically upwards in $t$ seconds, where $x = 100t - \frac{25}{2}t^2$. The maximum height reached is: (in $\text{ m}$)

The function $f(x) = 2x^3 - 15x^2 + 36x + 4$ is maximum at $x=$ ......

$\max _{0 \leq x \leq \pi}\left\{x-2 \sin x \cos x+\frac{1}{3} \sin 3 x\right\}=$

Let a function $f(x) = \begin{cases} -\ln(3x - [3x]) & ; 3x \neq n, n \in N \\ \ln(\operatorname{sgn}(3x)) & ; 3x = n, n \in N \end{cases}$,where $[.]$ and $\operatorname{sgn}(x)$ denote the greatest integer function and signum function respectively. Then the number of points where $f(x)$ is minimum in $x \in (0, 5)$ is: