My brother is an alumnus of IIT Madras. Nagendra and Shanthi Pavan were his favorite professors who taught courses in undergrad. It’s more likely that these professors have not given GATE. If you had gone through their profiles they have pursued their higher studies in foreign directly after their B.Tech in IITM. Both of them have got their PhDs from Columbia University, which is an Ivy League University.
Also, taught by the best professor then in VLSI (Dr. Radhakrishna Rao) would have quickly urged them to earn a Ph.D. from the "best" colleges in the world rather than just in India.