hi, no you cant register for mop up if you didnt get selected for 1st and 2nd counselling.

No.. mop up round is a special counselling done to fill the vacant seats left. The candidates who haven't got seat in Round 1 and Round 2 counselling , are given direct opportunity to participate in mop up round..
Candidates who have got seat in round 1 and round 2 or who have rejected the seat which they were getting in round 1 and round 2, or who have got a seat in all india quota counselling/or someither counselling are ineligible to participate in mop up round..main qualifying criteria remains the same as that of round 1 and round 2..

Hope you understood..

Good luck..

If you don't have cutoff mark for initial round counseling then you can not go for mop up round.but if you have resister for 1st round and don't get any seat then you can go for mop up round