If [p] means the greatest positive integer less than or equal to p, then $$\left[ { - \frac{1}{4}} \right] + \left[ {4 - \frac{1}{4}} \right] + \left[ 3 \right]$$     is equal to?

Solution (By Examveda Team)

Given [p] means the greatest positive integer less than or [p] equal to p
$$\eqalign{ & \Rightarrow \left[ {\text{p}} \right] = {\text{ p}} \cr & \Rightarrow \left[ -{\text{p}} \right] = {\text{ p}} \cr & \Rightarrow \left[ { - \frac{1}{4}} \right]{\text{ + }}\left[ {4 - \frac{1}{4}} \right] + \left[ 3 \right] \cr & \Rightarrow \frac{1}{4} + 4 - \frac{1}{4} + 3 \cr & \Rightarrow 7 \cr} $$