Yes you can , there are plenty private colleges in West Bengal. If you wish to know about some good private Engineering colleges then there is

1. Heritage Institute of Technology

2. Meghnad Saha Institute of Technology

3. Techno India University

4. Amity University

5. DR. B.C.Roy Institute of Engineering etc.

https://engineering.careers360.com/colleges/list-of-private-engineering-colleges-in-west-bengal

Private Pharmacy Colleges which are good

1. Guru Nanak Institute of Pharmaceutical Sciences

2. NSHM Knowledge Campus Kolkata

3. Dr. B.C.Roy Institute of Pharmaceutical Sciences

4. Gupta College of Pharmacy

Good luck!!