Though my own taxes help fund the IITs, and I never was hard-working enough to get through the JEE, I'm happy that we have the IITs setting at least some kind of an example for the rest of India. I am disappointed by the idiots filling teaching positions in most other colleges.
> do they not have a duty to give back to the people ?
I hate this attitude, not just in India, but anywhere in the world. Like Kennedy's "ask not what your country has done for you...". To start with, their own parents paid taxes to support the IITs too. Do we have a way of making a balance sheet for how my taxes were utilized? How much have I lost to supporting corruption? How much have I lost to supporting undeserving candidates who got in through reservation?
In case of IITs, you are, of course, neglecting all the private funding it gets.
> brain drain is a serious problem for countries like India.
Many Indians who have left have gone on to accomplish great things. Do you think they would have accomplished even 1% of that, had they stayed in India? Brain drain is not India's problem; it is an avenue for opportunity for many Indians. India's problem is corruption and unfettered democracy.