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Well brother, I can understand your situation. I know you have worked hard for JEE advanced but I believe with 3.6 category rank you won't be getting any decent IIT which I can recommend you.
Though with OBC, there might be an increased chance of your's getting a seat but with such a rank it is very hard to get.
As, opting a very low rank IIT core branch will bring nothing good for you which lags even the permanent faculty and infrasture to nurture you.
So, I would suggest you to prefer state engineering colleges or decent NIT's.
Also, I would recommend you to do take part in JoSAA and go to through all the round even the spot round. May be, some good fortune can turn your destiny.
Aspirants can check the JEE seat matrix in this ebook. Know about the number of category-wise seats offered by IITs, NITs, IIITs and GFTIs.
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