M.Sc. in Mental Health Nursing 

at Dr MGR Educational and Research Institute, Maduravoyal

Yes, Dr MGR Educational and Research Institute offers a Bachelor of Science (BSc), in various specialisations at the UG level. This full-time programme extended over three years. Candidates interested in pursuing a BSc can refer to the following table for more information:

NOTE: The above information is as per the official website. It is still subject to change and, hence, is inductive.

B.E/BTech, B.Arch, BBA, MBA, and MBBS are among the popular courses offered by Chennai's Dr. M.G.R. Educational and Research Institute.
Diploma programs in mechanical, production, automobiles mechatronics, plastic molding, CSE, IT, ECE, civil engineering, and chemistry are also available at the institute. 
Additionally, the institute provides undergraduate degree programs in BDS, B.Sc., BPT, B.Com, BCA, B.Ed, and M.B.B.S.  
There are fifteen specializations available in the four-year B.Tech normal course. Six specializations are available in the B.Tech part-time and lateral entry programs. 11 specialties are available for the B.Sc. degree. 
The institute offers online and offline application options, an admission exam, and a flexible credit-based system.

That depends on what you mean by "Directly" I suppose that you mean without JEE/ NEET, and if thats so, then yes you surely can based upon your 12th percentage. But its highly recommendable that you appear for JEE/NEET as it opens doors for other Nationally Recognized colleges like NITs and GFTIs and if you have already given and not getting any college than yes you can surely gain an admission by 12th percentage basis  in this college.

Dr. M.G.R. Educational and Research Institute admissions are open online for various courses. Till now, no schedule has been released by the university. Since the application portal is live, candidates can apply online for their preferred course.The university conducts entrance exams to shortlist candidates for various courses. DR MGR Educational and Research Institute offers more than 20 courses across various schools, such as the Faculty of Engineering and Technology, and the Faculty of Humanities and Science, among others.