IIT Madras conducts its own entrance exam, the Humanities and Social Science Entrance Examination (HSEE) to admit students for its various MA and Ph.D. programs. But you need to understand what your expectations are and what you want to do after the program.
If you want to do higher studies in the field after graduating, then it is a decent program. In terms of job placements on campus, it may not fulfill your expectations. Take a look at some placement statistics for the MA program for the year 2019-20 for better clarity.
Thus many students opt for higher studies or prepare for civil service examinations after studying here.