You didn't mentioned in which stream you want to take admission in Government i.e., in Professional course(BTech, BBA, Medical etc) or in general courses (BA/BSC/BCOM). Now for most of the professional courses you have to qualify the entrance examination, either national entrances or state entrances. For example, if you want to seek admission in college of Tamilnadu which accepts JEE MAINS score you have to qualify that, if there are colleges which accepts state level entrance score then you to apply according to that. But for general course, in general there are no entrances in Tamilnadu or Bangalore. You can take admission based on your 10+2 score.

I hope this answer helps. All the very best for your future endeavors!