My UPSEEE LEET general rank is 3966. My BCGL rank is 375. Can I get any good private or govt. college?

A UPSEE LEET general rank of 3966 and a BCGL rank of 375 is not a good rank for a good government college. However, you can get fee waiver seats in good private colleges and also in Rajkiya Colleges. 

Some good private colleges in Uttar Pradesh include: 

Amity University, Noida

IIIT Allahabad, Allahaba