University of Madras

Madras University offers BA in Criminology and Police Administration through distance.

Yes, visit the below link for all the details related to the course:
https://www.shiksha.com/humanities-social-sciences/course/b-a-in-criminology-and-police-administration-institute-of-distance-education-university-of-madras-chepauk-chennai-289332

Eligibility for B.A. in criminology and police administration in UNOM is:
The candidate must have passed his/her 10+2 from a recognised board. Admission is based on the marks obtained in 10+2.
For more details: https://www.shiksha.com/humanities-social-sciences/course/b-a-in-criminology-and-police-administration-institute-of-distance-education-university-of-madras-chepauk-chennai-289332

You can refer:
https://www.shiksha.com/arts-fine-visual-performing/music/course/bachelor-of-music-institute-of-distance-education-university-of-madras-chepauk-chennai-289350

Yes, it is UGC recognised and its valid.

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