University of Madras

As per NCTE norms, regular teachers working in primary, middle, secondary or higher secondary schools in Tamil Nadu, recognised by State / Central government, with a minimum of two-years teaching experience are only eligible for admission into Annamalai University distance education B.Ed course.

Ramanujan Institute of Advanced Studies in Mathematics (RIASM)
Entrance exam syllabus will cover your undergraduate syllabus fully. Two mark questions will be asked in general. Selection will be depended on your undergraduate marks and entrance marks
http://www.unom.ac.in/index.php?route=admission/cbcssyllabus

Hi Darshini are you asking for Madras University distance education or regular college?

Yes, you certainly can apply for M.Sc a year late without any issue. You could be asked to produce a document stating reason for gap in academics.