Yes you can get privet college , there are many private college in westbengal . You can also find in your local area also.  The cutoff also vary in which course which department you wants to study

As per your rank some colleges are

Dumkal Institute of Engineering and Technology, Murshidabad

Bengal College of Engineering, Durgapur

Modern Institute of Engineering and Technology, Hooghly

IMPS College of Engineering and Technology, Malda

St Thomas College of Engineering and Technology, Kolkata

Dr Sudhir Chandra Sur Degree Engineering College, Kolkata

NIT Kolkata - Narula Institute of Technology

You can aslo predict your college as per your rank from the below link .
https://www.careers360.com/wbjee-college-predictor

Thank you. I hope this answer helps you.

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