B.E. Automobile Engineering is a 4 years’ graduate degree program, the minimum eligibility is 10+2 class with Physics, Chemist, y and Math from a recognized school board or its equivalent exam. Top colleges in Bangalore offering B. Tech in Automobile Engineering are

• Dayananda Sagar College Of Engineering - DSCE
• School of Engineering and Technology, Jain University
• Faculty of Engineering and Technology, M. S. Ramaiah University ...
• New Horizon College of Engineering - NHCE
• Hindustan Aviation Academy

Hope this may help you. 

Dear aspirant, you can study Automobile Engineering from Bangalore by writing entrance exams related to the colleges you want to join and can get admission into it. You can write KCET exam also to get admission.

Click below links to get more details about your query.

https://engineering.careers360.com/articles/kcet-eligibility-criteria/amp

https://www.careers360.com/exams/kcet

All the Best.

Hy aspirant,
The choose you opt is the basic Field as many streams come through this mechanical engineering. It's like the sub-branches of mechanical engineering. So if you are wishing to opt for automobile engineering you can go for it.
Here are some colleges in Banglore for automobile engineering

• The Oxford college of engineering
• Dayanand and sagar college of engineering
• Hindustan aviation academy

Wishing you luck