Yes, you can try again in the second round of counseling, keep yourself updated about the counseling deadlines and procedure so that you don't miss out on anything.

Good Luck!

Dear,

Yes it is possible you can alloted in management quota. On the bese of your rank you will have a chances of getting the seat in the private college compare to government college 

Please do it as soon as possible. First know the procedure then please go head.

I hope you catch my point.

ALL THE BEST.