Mathematics - Continuity - Differentiability Question with Solution | TestHub

On $[0,2\pi ]$, let $f(x)=\lfloor \sin x\rfloor +\lfloor \cos x\rfloor$ for $0\le x\le \pi$, and $f(x)=\lfloor \sin x\rfloor -\lfloor \cos x\rfloor$ for $\pi <x\le 2\pi$. Match: (A) number of discontinuities; (B) number of interior points $a$ where ${\lim }_{x\to a}f(x)$ does not exist; (C) number of nondifferentiability points; (D) if the minimum is $m$, then $|m|$. Values: (P) 2, (Q) 3, (R) 4, (S) prime, (T) neither prime nor composite.