You can take part in both All India Quota (AIQ) and State Counselling separately. Both have independent processes. If you get a seat in AIQ Round 2, you can still participate in state counselling, but if you accept/join the AIQ seat, you must leave the state seat. Upgradation means you can float your seat and wait for a better option in the next round.
And for Round 3 (Mop-Up round), whichever seat you are allotted finally (AIQ or state), you must report directly to that college and complete admission formalities.
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