I've scored 45 in accountancy, 54 in business studies, 87 in economics, 81 in English & am from general caste, am I eligible for B.Com (H)?

Yes there is a chance that you can get addmission 

Minimum Eligibilty is 75%

Realistic admission cutoff  is 90%

It's about 85 percent 

No such information is present on internet officially or publicly of this year as well as previous years. It would be good to contact goneka college and ask for your queries 

The total fee for the B.Com (Hons.) programme at Goenka College of Commerce and Business Administration, Kolkata is approximately INR 3,780 for the entire 3-year course.