The fundamental period of the function $f\left(x\right)={\cos }^{-1}\left(\mathrm{cos\pi }x\right)+\left|\sin \left(\mathrm{\pi }x\right)\right|+sgn\left(x^2-10x+30\right)+2021\mathrm{sin\pi }\left[x\right]$ is

[Note: $\left[x\right]$ denotes greatest integer less than or equal to $x$ and $sgn x$ denotes signum function of $x$.]

A travelling wave is described by the equation $y\left(x,t\right)=\left[0.05\sin \left(8x-4t\right)\right] \mathrm{m}$. The velocity of the wave is:

[All the quantities are in SI unit]

Let $f\left(x\right)=\sin x+\cos ax$ be a periodic function. Then,

The function $f\left(x\right)=\left|sin4x\right|+\left|cos2x\right|,$ is a periodic function with a fundamental period