JEE Main

For Biomedical Engineering, you can either be a student who has done PCB in class 12th or PCM in class 12th. As for admission, it varies from university to university. Some of them offer admission entirely on the basis of JEE exam, some offer admission on the basis of their own tests, some offer admission on the basis of the above mentioned both criteria and some offer admission just on the basis of marks in class 12th.
You can check the websites of some good universities like IITH, LPU, SRM, MU, etc. for more details of the course and eligibility.
Most of these places have good infrastructure, good faculty, environment conducive to learning and even placements are good.
Good luck.