The period of $f(x)=\sin 5 x+\cos \sqrt{3} x$ is :

$\frac{2 \pi}{5}$ $\frac{2 \pi}{3}$ $\frac{2 \pi}{\sqrt{3}}$ None of these

None of these

Period of $\sin 5 x$ is $2 \pi / 5$ Period of $\cos \sqrt{3}x$ is $\frac{2 \pi}{3}$ for the period of f(x) LCM of $2 \pi / 5$ and $\frac{2 \pi}{\sqrt{3}}$, which doesn't exist. Hence f(x) is non-periodic Hence (4) is the correct answer.