Automobile Engineering or Automotive Engineering is a part of Mechanical Engineering. Through the application of automotive technology, the course offers specialisation in vehicle designing, repairing, testing and assembling. In this programme, one can also learn safety engineering, quality management and control, automotive analytics as well as assembling and installation of various automobiles. BE/B.Tech in Automobile Engineering is a 4-year programme

I am providing you wih a list of these colleges:-

• Indian Institute of Technology Bombay
• Indian Institute of Technology Delhi
• College of Engineering, Pune
• Indian Institute of Technology Roorkee
• RV College of Engineering, Bangalore
• Chaitanya Bharathi Institute of Technology, Hyderabad
• Coimbatore Institute of Technology, Coimbatore
• Lovely Professional University, Jalandhar

In the IITs, for cutoff you can check the official Josaa counselling website to have an idea of the opening and closing ranks .

Here is a link of that https://josaa.nic.in/webinfocms/Public/View.aspx?page=71

For other colleges yu can visit the webite of those colleges to know from which engineering entrance exam they consider to take admissions in their college.