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Hello,
As far as I think, a mop up round is the councelling process where respective seats are reverted back to the states after the end of All India 15 percent quota counelling. The seats of the respective states which are not filled by 1st and 2nd rounds of counselling of All India quota are then filled up in mop up rounds so I think that for the mop up round you can only fill colleges from your own state (for the one for which you have a domicile) and not in other states. But for private colleges of other states, you can still apply.
Hope this helps.
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