Greetings, 

Hereby I am listing out the names of government colleges where you can apply . As you have not mentioned your scores I am listing out government colleges which provide automobile engineering course .

JADAVPUR UNIVERSITY , KOLKATA 

VEERMATA JIJABAI TECHNOLOGICAL INSTITUTE , MUMBAI 

NATIONAL INSTITUTE OF TECHNOLOGY , WARANGAL 

COLLEGE OF ENGINEERING , GUINDY 

MADRAS INSTITUTE OF TECHNOLOGY , CHENNAI 

NATIONAL INSTITUTE OF TECHNOLOGY , PATNA 

MAULANA ABUL KALAM AZAD UNIVERSITY OF TECHNOLOGY , KOLKATA 

LD COLLEGE OF ENGINEERING , AHMEDABAD 

SHIVAJI UNIVERSITY , KOLHAPUR 

DAYALBAGH EDUCATIONAL INSTITUTE , AGRA 

UNIVERSITY OF MUMBAI , MUMBAI 

RAJASTHAN TECHNICAL UNIVERSITY , KOTA 

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY , HYDERABAD 

MGR EDUCATIONAL AND RESEARCH INSTITUTE , CHENNAI 

MAHATMA GANDHI UNIVERSITY , KOTTAYAM 

UNIVERSITY INSTITUTE OF TECHNOLOGY RAJIV GANDHI PROUDYOGIKI VISHWA VIDYALAYA , MADYA PRADESH 

GOVERNMENT COLLEGE OF ENGINEERING AND RESEARCH , PUNE 

GUJRAT TECHNOLOGICAL UNIVERSITY , AHMEDABAD 

UNIVERSITY COLLEGE OF ENGINEERING BHARATHIDASAN INSTITUTE OF TECHNOLOGY , TAMIL NADU 

GOVERNMENT ENGINEERING COLLEGE , RAJKOT 

I hope this helps . For further doubts do drop a comment