Prof. Ramkrishna More Arts, Commerce and Science College

Yes, you can get admission for MCA without giving the entrance exam by going for direct admission process.
the only requirements are that you should have already passed BCA or other equivalent examination.
for merit based direct admission you should have the specified minimum aggregate by the institute which is generally 60% in you BCA.
You can also try for the college's reserved management Quota Seats but it could cost you dearly.

As per the information available on the college website, the college does not offer MCA course. Please visit http://www.pdearmacs.edu.in/ in the department section.
However, your experience about the college is not too satisfactory. Please post your review on shiksha.com so that maximum of the students could benefit from your experience.

Course Duration of Master of Science [M.Sc] (Zoology) is 2 Years.
Age - No age limit
Minimum Percentage - 50%
Subjects Required - Bachelors Degree with Medical and Allied Science, Bioscience and Life Science as compulsory subjects.

As you have completed your B.Com , you are eligible to apply for M.Com.

Yes, there is an entrance test. you would get the application form in the official website of the college. I guess it will be out by February next year, do keep yourself updated with the date.