My rank is 6500 (GEN) whether should i drop or carry on from this rank .

If I continue then can I get any core sector in top 10 IIT.

Although probablity is less to get all those top 7 IITs. in first two round of counselling.
But you should register for counselling, may be you get a good branch because...counselling can be upto 4 round ...so have try. ...