If you want to take admission in engineering you should appear for below entrance exams

1- JEE (Main+Advanced)- In order to take admission in NITs/IIITs/GFTIs you have to appear for JEE Main exam.

To take admission in IITs you have to qualify for JEE Main exam in order to appear for JEE Advanced exam. 

In order to be eligible 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-  In order to be eligible for this exam you should have 75% aggregate marks in Physics, Chemistry and Mathematics  in your 2th class. Also, in each of the 3 subjects, they must also secure 60% marks separately

3- VITEEE- In order to be eligible for this exam you should have scored an aggregate of 60% in Maths, Physics and Chemistry in 10+2 and for SC, ST, J&K, North Eastern states you should have scored an average 50% marks in Physics, Maths and Chemistry in 10+2 or its equivalent exam.

There are other private exams as well like SRM, Manipal and Amrita in which you can apply. 

You should also appear for your state level entrance exam to take admission in state government colleges.