Which is/are correct

If  $F\left(x\right)={\left(f\left(\frac{x}{2}\right)\right)}^2+{\left(g\left(\frac{x}{2}\right)\right)}^2$ where $f"\left(x\right)=-f\left(x\right)$  and  $g\left(x\right)=f\text{'}\left(x\right)$ and  $F\left(5\right)=5$ then  $F\left(10\right)$ equals 5

If  $\left[\sin x\right]+\left[\frac{x}{2\pi }\right]+\left[\frac{2x}{5\pi }\right]=\frac{9x}{10\pi }$ then the number of solutions of this equation in $(30,40)$  is 1

Let  $a,b,c\in [0,\pm 1,\pm 2].$ The number of ordered pairs  $(a,b)$ so that $f\left(x\right)=ax+b$  is self inverse function from  $ℝtoℝ$ is 5

If real function satisfies  $f(10+x)=f(10-x)$ and $f(20-x)=-f(20+x)$  for all  $x\in R$ then  $f\left(x\right)$ is odd periodic function