First of all congratulations for getting 87 percentile in jee mains. In this percentile you can get seat in many good colleges.

1) You can apply for nits and iiits and there are very good chances that you can get seat.

2) This option is for back-up but you have to sit in state colleges councilling session. And there you definitely get a seat with your score and in a good college.

Note :- Before sitting in councelling prepare a list of college ranking in India (don't you worry I've solution for that also you can go through this link https://engineering.careers360.com/colleges/ranking). And fill college in descending order of rank (i.e. first highest then second highest and so on).

Hello,

Congratulations for your score you achieved in JEE Mains,

You can check our College predictor tool to get the list of colleges you are eligible for, you just have to fill the required details and then you will get colleges list.

Link for College predictor tool: https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer