Computer science and bio mechanical

It is always suggested to do your UG from India. And India has top engineering colleges than outside our country for B tech. Still I am sharing few names of colleges. These are the requirements to apply in Harvard University for Btech. Check here: https://college.harvard.edu/admissions/application-requirements

You will be required to give SAT exam and most likely English Proficiency exam. The requirements depends on each college as it can vary.

You can check the MIT selection process here. Link: http://mitadmissions.org/apply/process/selection
Good Luck.