Hello Aspirant,
Management seats are available in private colleges and not in government colleges, whereas the 3rd round of counselling that you are talking about is for admission into government medical colleges.
So it is good that you have already taken admission in a private college which you can use as your back-up option in case you do not get a government college.
You will not lose your management seat if you appear for Round-3 counselling.
Hope this helps.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile