Hey bro, with 2 lakh rank in Jee mains, you can't expect a good government college, and for a best private college, you should fill their form and had given their entrance exam. But now the time had gone for all that.

And for now, it's upon you, which colllecyou want to take according to your preferences like the place near you, your budget, your choice, course which you want to opt, etc.