In order to take admission in engineering colleges you can appear in National, State and private level colleges. Below are the names and eligibility criteria of the exam

1- JEE (Main+Advanced)- To take admission in IITs/NITs/IIITs and GFTIs make sure you should have 75% marks in your board exam or you should be in top 20 percentile. For SC/ST you should have 65% marks.

2- BITSAT- You should have secured at least 75% aggregate marks in the qualifying examination with Physics, Chemistry and Mathematics. You should have scored 60% marks separately in each of the three subjects.

3- VIT- You should have secured 60% marks in Physics, Chemistry, Mathematics in 12th class. SC/ST categories and North-East should have secured an aggregate of 50% marks in Physics, Chemistry, Mathematics.

4- Manipal- You should have scored 50% marks in Physics, Mathematics and any one of the optional subjects in class 12th.

5- Amrita- You should have aggregate marks of 60% in Mathematics, Physics and Chemistry with not less than 55% in these three subjects individually.

To know in detail you can refer below link https://engineering.careers360.com/exams

Good Luck!!