Given a set of n rays in plane, we define a reversal as the operation of reversing precisely one ray obtaining a new set of n rays. If n=2001 and k reversals are performed such that all the rays are reversed, then a possible value of k is?

Dear Student
There are n rays.
If we reverse all of them, we would have a complete reversed set after n reversals. After that any reversal that we perform has to be undone with another reversal to obtain complete reversal.
We can have a complete reversal after k reversals if k = n + 2m (m ∈ N). i.e., k could be some number greater than (or equal to) n and of the same type (even/odd)
So n = 2001 then k = 2001 + 2m
So k = 2011

Thanks