Hi Naveen,
Both IIT Bombay and NIT Trichy belong to the best colleges in India. I would also like to suggest you that just don't run for the name of the college. After working for three-four years, it won't matter whether you studied from IIT Bombay or NIT Trichy. Which branch you chose is more important. This is the time when you decide what you want to do for your whole life. If you some branch that doesn't interest you will regret it for the whole of your life. Till that time it will be totally impossible for you to change your career and you will be among the unemployed engineers of our country. Choosing your field is really important. Do it wisely.
Chose the field that really interests you the most.
I hope I was able to guide you properly.
All the best for your future
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