In order to take admission in automobile engineering you can appear for the entrance exam of engineering.

You can appear for JEE, SRM, Manipal entrance exam in order to take admission.

You can check the top colleges of automobile engineering below 

National Institute of Technology Warangal

SRM University, Chennai

Manipal Institute of Technology, Manipal

PSG College of Technology, Coimbatore

Lovely Professional University, Phagwara

SASTRA University, Thanjavur 

To check complete list you can refer below link

Top colleges for Automobile Engineering