Yes , scholarship is provided in Tata University. Follow the link given below
https://admissions.cornell.edu/apply/international-students/tata-scholarship
And yes , there is an entrance exam too
The fee structure depends upon the university which you are talking about

Dear Syed

Tata Institute of Fundamental and Research will not give the entry for the 12th passed students for doing their UG degree, it has it's own entrance exam called as TIFR entrance exam which is for the entrance for the student's who want to do their study in M.Sc, PHD or any type of research in any of your respective relevant field.

All the best

TIFR Mumbai

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