Each year Texas Instruments (TI) India sponsors some students for the analog electronics MS program at IIT Madras. One of my friends went through the whole process and here are some of the useful snippets of her experience.
In the interview, they are looking for your thought process and your approach to the problem rather than the exact correct answer as my friend did give a wrong answer but still got selected.
Also, the professors and the interviewers were very helpful and will guide you. The questions in the tests and the interviews will test you very thoroughly so you should have a stronghold over the subject. You can go through the preparatory materials posted on the website and the electronics book by Sedra and Smith.