JEE Math Practice Question

For each t $$ \in $$ R , let [t] be the greatest integer less than or equal to t Then $$\mathop {\lim }\limits_{x \to 1^ + } {{\left( {1 - \left| x \right| + \sin \left| {1 - x} \right|} \right)\sin \left( {{\pi \over 2}\left[ {1 - x} \right]} \right)} \over {\left| {1 - x} \right|.\left[ {1 - x} \right]}}$$

1. A.equals $$-$$ 1
2. B.equals 1
3. C.equals 0
4. D.does not exist