Yes, Madras Institute of Technology (MIT) is a government engineering college located in Chromepet, Chennai, India. In fact, it is one of the three government engineering colleges of the state of Tamil Nadu (College of Engineering, Guindy and Alagappa College of Technology, Guindy being the other two) to be controlled directly by the state university, Anna University.
It was initially established as the first self-financing engineering college of India by offering a three-year degree called DMIT (Diploma in Madras Institute of Technology) in specializations such as Automobile Engineering, Aeronautical Engineering, Instrumentation Engineering, Production Engineering, etc.
The eligibility for the DMIT course during that time was B.Sc, i,e only science graduates could apply for the diploma in engineering. Later the diploma was converted to a B.Tech and currently, the eligibility is 12th standard as the case with all other engineering colleges in the country.
Madras Institute of Technology is like any other government engineering college and all the eligibility criteria and procedures are similar to other colleges.