Yes, you will able to get admission in a private college of Pune, but for admission in a private college there is no need of JEE mains score. You can get admission without JEE mains score, But if you want to get admission in mit pune or some good private colleges, then they will give you scholarship on the basis of your rank in JEE mains. If you got good marks then you will be eligible for scholarship.

Best of luck.