Dear aspirant,

As per your rank in obc category that is 6.5k so you will not be able to get non core branches in top colleges like Jadavpur University, institute of engineering and technology, heritage institute of technology,technoindia Salt Lake.

But you may hope or rather stand fair chances for non core branches in haldia institute of technology,technoindia university, future institute of technology and other parallel colleges.

For more information you can check out the link given below-

https://engineering.careers360.com/articles/wbjee-cutoff