Hello Aspirant.

As you've mentioned that you've scored 82 percentile in JEE main and have also mentioned your rank. Considering both the factors and assuming that you're a general candidate, you cannot get any government institution based on this rank as your rank is too high to get enrolled into any government college.

You need to have any quota, for admission into any government college at this rank.

To know which colleges you can get please click on college predictor