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Hey! 

I can tell you of some private colleges and universities in India which are good for automobile engineering.

Vellore Institute of Technology (VIT), Vellore – It is known for its engineering curriculum and research.
SRM Institute of Science and Technology, Chennai – Offers good placement and infrastructure.
Manipal Institute of Technology, Manipal – Good labs, experienced faculty, and practical learning.
Chandigarh University, Punjab – This university offers an amazing Automobile Engineering course and their course covers everything from designing car parts to testing vehicles for safety and students get hands-on experience through special labs like AutoCAD with CREO PTC, Automotive Electronics and Vehicle Maintenance centers. The programme also includes new trends like Electric and Hybrid Vehicles, Automation, Green Manufacturing, and Alternative Fuels like Biodiesel and Hydrogen, they also have industry labs with Mahindra, Honda, MG Motors; global exposure; high placements; and ABET, NBA accreditations.

Chitkara University, Punjab – Provides automobile engineering course with projects and internship support.

I will suggest Chandigarh University because I have really heard a lot about it, rest you can visit the universities, explore the campus, see infrastructure, talk and interact with teachers and students and then you can decide about it more effectively.