Hello student i request you to please help me with the State or City you prefer as there are many government engineering college and I can't name all of them here.

Some of the best government engineering college with fees for mechanical engineering are as mentioned below -

1. IIT Bombay - 908,400
2. COEP Pune - College of Engineering - 339,450
3. IIT Madras - Indian Institute of Technology - 804,400
4. MSU Baroda - Maharaja Sayajirao University of Baroda - 20,880
5. DTU Delhi - Delhi Technological University - 780,800
6. JMI New Delhi - Jamia Millia Islamia - 26,910
7. LDCE Ahmedabad - LD College of Engineering - 8,490

Fees vary from college to college i request you to please help me with your preferable college in which you're willing to pursue mechanical engineering so that I can check and provide you the exact information about admission process, academic fees and eligibility requirements.

For more details refer to the link mentioned below - https://engineering.careers360.com/colleges/list-of-mechanical-engineering-colleges-in-india

Feel free to comment if you've any doubt

Good luck