Can a B.A. (general) student pursue MA in mass communication from Jadavpur or Calcutta University?

No, you cannot. Calcutta University or Jadavpur University doesn't allow a Masters unless you have a honors degree. However, you can try distance education in mass communication.

To apply for Jadavpur University in M.A. Mass communication you need to have B.A. (Hons) degree. Calcutta University does not offer mass communication course.