Hi aspirant, your performance is nice in the JEE mains, I would like to suggest this below mention link where you can get all the detailed information about your doubts and you can plan accordingly.

I wish you all the best for your future.

https://www.google.com/amp/s/engineering.careers360.com/articles/list-of-government-funded-technical-institutes-gftis/amp

Hi aspirant

You can only get if you belong to some reserved category like SC/ST/PWD otherwise not.

You can apply for  state engineering colleges of your home state through state counselling.You may get that.

You can use college predictor tool to predict you colleges based on your score,category,home state .Visit here:https://engineering.careers360.com/jee-main-college-predictor 

Hope this was helpful.