JEE Advanced 2013 · Paper 1, Mathematics question 44

Let $f(x)=x^2-x\sin x-\cos x$, an even function with $f(0)=-1$.

Monotone. $f'(x)=2x-\sin x-x\cos x+\sin x=x(2-\cos x)$, positive for $x>0$. So $f$ increases from −1 to ∞ on $(0,\infty)$: one root; by symmetry another for $x<0$.

Two points.

(C)