Are Indian educational institutions world class?

A few days back I had a engrossed discussion with my friend regarding whether Indian institutions are world class or not. There were many aspects to this and although either one of did not agree on each other arguments I found the discussion very insightful since it provided many alternative perspectives on how to look at things. Some of the points which were in my mind were -

1. There are many Indians going to top B Schools or top Tech Schools across the globe and making it big. How many people coming from the world to India for such programs?

2. Due to my interaction with one of the administrative staff at one of the top B schools of the US I came to know that they are looking for partner schools in India and China. But upon self introspection I thought what options would they have? How mature are Indian B Schools in order to establish such partnerships and provide a conducive environment to students coming from abroad. Only ISB and IIM A/B/C? If IIMs, I am sceptical about how would the collaboration work? Apart from the intellectual potential (which is also a big question now after reservations) and an "Indian" setup what else would these institutes would? IIMs have been there since long but why have they not been able to make it to the top B schools list despite having the best and the smartest brains of India? I think it is the bureaucracy, reservations, curriculum though best in India but it still needs to be more flexible and experiential learning needs to be encouraged more. This said I would love to highlight that guys please don't treat me as a mere critic of the best schools of India. IIMs are excellent institutes and just for record, I was not given an admission into any of the IIMs despite my efforts but even today I would perhaps take pride being an alum from anyone of these institutes.