I have done B.Sc Zoology & Chemistry but next M.Sc Zoology completed what i can do this exma CSIR UGC NET
Yes you can do. You can apply for CSIR NET exam with your post graduation eligibility. They don't look about the cross majors. It is one of the toughest exams in India and at the same time best exam which can give you a chance to get a lecturer job in colleges and Junior research fellow position in research institutes and colleges with a stipend of 31000 with HRA.
All the best.