M.Sc

Yes, You should continue M.Sc in bio-tech. There is no age limit for M.Sc. Okay. You want to get admission in M.Sc. You apply for IIT JAM and well prepare for it. If you get a better score. You eligible for IIT college in India or IISC and IISER. These colleges give admission by jAM only. Okay If you don't interest to write jam then some college conducting there an entrance exam for M.Sc. You continue M.Sc with those exams also.
All the best. Hope this helps.

Yes, you can do the M.Sc. Hons. Mathematics after your B.Tech. The eligibility criteria of LPU is given below for reference only.
Eligibility criteria : Pass with 55% aggregate marks in Bachelors degree (any discipline) (with Mathematics as a subject) or B.Tech. Or B.E. Or B.Sc. (Engineering) or equivalent.

MCC is affiliated to University of Madras. The admission in M.Sc statistics is based on merit in the qualifying exam (B.Sc.).