Dear Aaron,

Yes, you need to appear for the entrance exam in order to take admission.

You can check the top colleges below

National Institute of Technology Warangal

Jadavpur University, Kolkata

Manipal Institute of Technology, Manipal

SRM University, Chennai

PSG College of Technology, Coimbatore

SASTRA University, Thanjavur

Lovely Professional University, Phagwara

To check the complete list you can refer below link

https://engineering.careers360.com/colleges/list-of-automobile-engineering-colleges-in-india

Good Luck!!