Yes you can apply for MSc after completing BSc. MSc can be done by research or by paper. Very few colleges offer Msc by research but you can easily get admission into MSc by paper in india. You need to apply for each college spearately as there are no centralised entrance exams. Some good colleges have entrance exams and you need to pass them. So please search the college you want and type of MSc. they provide. 

All the best