Indian Statistical Institute (I.S.I.), Chennai Mathematical Institute (C.M.I.) and Institute of Mathematics and Application (I.M.A.) can be regarded as three Indian institutions that provided world class mathematics course at undergraduate level. The B.Stat Course at I.S.I. is also world famous. The courses at C.M.I. and I.M.A. have computer science as second major.
Each of these three institutes conduct entrance test at the month of May. The prospective students are expected to know more rigorous mathematics than the IIT's. Apart from High School math, the entrance test syllabus includes Math Olympiad curriculum- plane geometry, combinatorics, number theory, inequalities, functional equation, polynomials and more.
Indian National Math Olympiad qualified students are not required to take the Entrance test. They will directly appear for the interview. Yes, there is an interview after the entrance test where students are asked math related questions.
The entrance tests are on Mathematics only. There is no age bar and non science students may also sit in the test provided he/she had pure maths in High School. The alumni of these three institutes are working in the most prestigious labs, universities and corporate sectors of the world. India hopes to regenerate it's mathematical fervor through state-of-art institutes like these.
Preparatory guidance for I.S.I., C.M.I. and I.M.A. entrances (and Math Olympiads) are difficult to find. Check out our website for some help.