Can I complete BA or B.Com in a year?

No this is not a valid degree today many university provide this type of program but their degree is not valid for job or higher study, they give you back date entry and there is no process to give backdate entry university maximum provide 4-5 month backdate not 2 year this is not possible this type

No.Degree programmes as you have mentioned are of three years duration in India. All the best.