With this rank it will be very difficult to get a branch in any of the IITs as the maximum closing rank for all the IITs in the lower branches falls in the range of 3500 to 4000 in OBC category rank. Thus, you should for admission in any NIT or IIIT as you might have a chance og getting a decent branch there if you have an equivalent rank in JEE Mains. Also you can try for private colleges like BITS and VIT. Hope this helps.

Hi there,
Hope you are doing well.
I am really sorry to say but with 6700 rank in JEE Advanced OBC Category, you can't get a seat in any of IITs
The final closing rank to get admission is 3829 for admission in IIT BHU B.Tech. + M.Tech. - Pharmaceutical Engineering & Technology

Hope it would help