You do not need to do any research at all. The proof of the pudding is in the eating. The best college to do the BTech Mechanical Engineering course is the best NIT in India, as of today, and this college is called the National Institute of Technology, Tiruchirapalli.
It is one of the oldest Regional Engineering Colleges, at least 80 years old now. The admission to this NIT, considered to be even better than the new IITs, happens through the JEE entrance examination every year. The placement record is fabulous and it enjoys a one hundred percent placement record from the time of inception.
The course is highly rated only because of its World-class Faculty and Students. As a sort of norm, at least 60% of the students go abroad, particularly to the USA for higher studies and they do very well. The Alumni network is so strong and the ecosystem of the college and the Mechanical Department is such that the interaction among the best of pan-India students is so good at any stage.
Their internship facilities are just too good. This college has a fabulous record of industry-institute collaboration. Apart from the BHEL unit which is situated just five kilometers from this college, the institution has a very wide network of industries that happily offer the best internship facilities.
In the next few years, it is hoped that with the New Educational Policy coming up in a big way, there will be a massive improvement in the standards of this prestigious institution.
Am not mentioning any other institute, as I would restrict my views to just one college.