Hello Tharun,

First of all congrats for grabbing such good options in premium institutions. Now the answer to you question depends on two things, one is whether you are very particular about the  college reputation or brand name.Second is your interest in the subjects you have mentioned. Only after these comes other aspects because it is you who is going to take up the course. Hence, if you concerned about the IIT  tag then you may go for it . This is also because IIT on a global platform is considered as highly reputed institution and is considered as India's MIT. But having said that you should also consider the courses you have got , your interest level in those. First when you take engineering physics , it is a fascinating field if you like physics. This course will be on core theoretical physics combined with its application which is engineering. Now this is basically like taking BS.c Physics from IIT. And as far as the placement is concerned, there wont be that many companies coming targeting only EP students. Most of them at the end of the day end up sitting for non-core placements with electrical or computer science students that too after gaining extra skills like programming but if you are really hardworking then you may end up getting a good job no matter what.. But if you an intention to study further , then you may enter into fields like Particle Physics, Nanophotonics, String Theory, Nuclear Science, Quantum Physics & Computing, Engineering Optics, Computational Physics, Biophysics, Astrophysics etc and even end up working in NASA. Coming to biotech, IIT does not emphasis much in it . If you like biology and would go for advance study abroad, then you may end up better than expected otherwise not much scope.Even for this course , you may end up in non-core placements , hence simply for IIT tag you can go it that matters to you, otherwise compared to this EE at NIT Trichy(which is a topmost NIT) has far better scope. Finally coming to naval and ocean engineering , if you want to work as a Naval Architect or Ocean Engineer, or if you have interest towards getting into aerospace field then this is the course.But as far as India is concerned the in this field the supply is more but demand is less,so again go for it if you are going to be persistent with it and is ready to do further studies. Conclusion, is that if you have good interest in these fields,placements in non-core fields does not concern you and want a rich learning experience go with IIT Madras because it is an old IIT. Old IITs are very rich in terms of the learning experience but if you want a top engineering branch and good placements in core field from a reputed institution then choose NIT Trichy, remember EEE can also help you work in tech field on a global level.

I have just provided a little insight into all the courses based on their scope , kindly research more about their syllabus , reviews from seniors, core areas , future growth, about the campus life  etc and take a well informed decision after thorough analysis . At the end of the day the decision is entirely based on your interests ,goals and situations .

All the best