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Avg in Btech CS is 5.5 and ECE is 4.8.
However , none have a max above 10lpa indicating no foreign placements(Which are $50K to $100K range)

Nevertheless , IIIT-H is good .Its placement details can be found here.

http://www.iiit.ac.in/placements/placement2008/quickglanceplacement2007_recruiters.php

Keep in mind that IIIT-H has just CS and ECE , so its natural that it'll have a good avg.
In Private Coll. vs Govt Coll. plz exclude BITS out of it.BITS doesn't follow the pattern which you have talked about.But you are largely right.

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