MCA

RCC Institute of Information Technology, Kolkata
West Bengal University of Technology, Kolkata
Jadavpur University, Calcutta
Meghnad Saha Institute of Technology, [MSIT] Kolkata
Techno India Saltlake, [TIS] Kolkata
These are the best colleges for MCA in Kolkata, for colleges offering MCA without mathematics, you need to check the college eligibility individually.

Mentioned below are the best universities offering MCA:
Pune University, Computer Science Department
School of Computer and Systems Sciences (Jawaharlal Nehru University)
School of Computer and Information Sciences (University of Hyderabad)
National Institute of Technology Tiruchirappalli (Department of Computer Applications).

Check out the article below for all the entrance exams for MCA:
https://www.shiksha.com/it-software/articles/top-mca-exams-in-india-blogId-13629

Masters of Computer Applications (MCA) is known to be as one of the popular course among aspirants to build their future in IT Industry, because of the vast career options that this programme holds. It is a three-year Post Graduate programme in the field of computer applications. The programmes main focus is on the development of latest applications with the help of various programming languages.
For entrance exams, check out the article below:
https://www.shiksha.com/it-software/articles/top-mca-exams-in-india-blogId-13629

College change or university change after the first year is completely dependent on college and university norms, some university allow it and some won't plus you need to have good scores in the first year to apply for the same. For further details, contact the college authorities.

http://www.nitt.edu/home/academics/fee_details/
You can refer to the above link.