JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 88

$|\sin4x|$ has period $\frac\pi4$ and $|\cos2x|$ has period $\frac\pi2$. The sum repeats at $\frac\pi2$. No smaller period works: $f(0)=1$ but $f\left(\frac\pi4\right)=0$.