Period of cos(x2) is

Let $\cos x^2$ has periodic $T \cos (x+T)^2=\cos x^2 \Rightarrow(x+T)^2=2 n \pi \pm x^2$

$\Rightarrow(x+T)^2 \pm x^2=2 n \pi$

Since it is a quadratic in T and if solved, T will never be independent of x. Hence it is not periodic function.

Hence (4) is the correct answer.