My friend is a PhD student at IIT Madras and shared his interview experience which is similar in all the branches.

Candidates are shortlisted based on written exams that make it easy for the panels to choose among the best. This exam comprises basic GATE-level MCQs and very few questions related to the department. The entire selection procedure is wrapped in 3-4 days. The written test is quite basic and is checked by research or teaching assistants. A few departments like applied mechanics have some difficult questions related to the discipline. But this is a rare occurrence.

Usually, the level of difficulty of the exam depends on the number of candidates. It’s advisable to go through the basic topics before attempting the written test and you are good to go.