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No, you can't get admission in IIIT Ahmedabad with this rank.

There are 20 IIITs you can wait until the JOSSA'17. You have got a good chance if you fall in a category.

Don't go for Vidyasagar University. You will never get placement. Try for another one. Another thing is, I was former student of VU MBA, and I didn't give CAT or MAT exam.

That depends upon the institution you want to join. Scope of Nursing and scope of MBA is totally different. So, one cannot get you qualification for other.

Closing rank for OBC category in JEE Mains of this college for (given rank may vary 2-3k):
Mechanical Engineering-70k
CSE- 72k
Civil Engineering - 75k
Electrical Engineering -75k
EC - 90k
Information technology- 95k
Industrial and production- 110k
All the closing rank is up to last counseling.

You can opt for mechanical engineering as it has good placements.