The period of $f(x) = \cos \left(\frac{x}{3}\right) + \sin \left(\frac{x}{2}\right)$ is (in $\pi$)

Consider the function $f(x) = \cos(x^2)$. Then,

Let $f$ and $g$ be periodic functions with the periods $T_{1}$ and $T_{2}$ respectively. Then $f+g$ is

Let $\alpha$ be the period of $3 \sin \frac{\pi x}{3} - \cos \frac{\pi x}{2} + \tan \frac{\pi x}{4}$,$\beta$ be the period of $\sin^2 \left( \frac{\pi}{7} + \frac{x}{4} \right) - \sin^2 \left( \frac{\pi}{7} - \frac{x}{4} \right)$,and $\gamma$ be the period of $\cos^4 x + \sin^4 x$. Then $\frac{\alpha \gamma}{\beta} = $

The period of $\cos(x + 8x + 27x + \ldots + n^3x)$ is

The period of $|2\sin 3\theta + 4\cos 3\theta |$ is