Shefali has given a pretty insightful answer to your question already, i'd also like to add that if you're treating Graduation in science(B.Sc.) as another option, most of the reputated colleges consider your score in 12th board exams or any equivalent course for the admission criteria.

Some of the colleges you must consider are DU, St. Xavier's, MU, AMU.

Dear Karan,

It is good to keep as much as option to get into top colleges of engineering as lot of competition is envolved in getting top colleges. 

Apart, from JEE exam you should appear for BITSAT, VITEEE, SRMJEEE, Manipal, Amrita and COMEDK.

To get admission in government colleges of your state you can apply for your state level entrance exam. 

There are many private colleges as well who consider JEE Main exam to provide admission. You need to apply for the application form seperately for them.

To know the colleges you can refer below link

https://engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-India-accepting-jee-main-score

Good Luck!!