As you have asked about the Tata Institute of Fundamental Research (TIFR) entrance exam, I am giving you information about it, check below for the details

Tata Institute of Fundamental Research Entrance Exam is conducted to provide admission to graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degreee in certain subjects.
The Graduate Programme at TIFR is classified into the following Subjects:
Mathematics
Physics
Chemistry
Biology, and
Computer & Systems Sciences (including Communications and Applied Probability) and Science Education

Eligibility

Candidates in the final year of qualifying degree can also apply
Mathematics:

For Ph.D: M.A./M.Sc./M.Tech
For I-PhD: B.A./B.Sc./B.E./B.Tech (Students already /completing an M.Sc degree by July 2016 are not eligible)

Physics:

For Ph.D.: M.Sc/M.S in Physics, or equivalent, on completion of programmess of duration not less than 5 years in total
For I-Ph.D.: M.E/M.Tech/B.Sc/B.S./B.E/B.Tech/B.Chemistry in Physics, Engineering Physics, or equivalent degree,
In addition - I-PhD candidates with four or more years of university education who clear the written test may be considered by TCIS for their PhD program

Chemistry:

For Ph.D: M.Sc./M.Pharm
For PhD: B.Sc/B.E/B.Tech/B.Pharm

TIFR Entrance Exam Syllabus
TIFR Entrance Exam consists of questions from the relevant subjects upto the level of Graduation.

TIFR Entrance Exam Pattern
TIFR consists of objective multiple choice type of questions from the relevant subjects.