IIT Eligibility

Yes, you are eligible for M.Sc. Mathematics through IIT JAM. While not eligible for NIMCET. The eligibility criteria of NIMCET is given below. Eligibility criteria : (I) B.Sc. / B.Sc. (Hons) / BCA / BIT / B.Voc. (Computer Science/ Computer Applications) of minimum three years full-time programme from a recognised University with Mathematics/ Statistics as one of the subjects
or (ii) B.E. / B.Tech. from a recognised university.

For NITs, you need minimum of 75% in 10+2 and you need to qualify JEE Mains paper 2. For IITs you need minimum of 75% in 10+2 and you need to qualify JEE Mains paper 2 and 1 and then JEE advance and then AAT to be eligible.

I would say you should join IIT Kanpur. IIT Kanpur placement stats are good and programming culture is also great there. IIT Roorkee is also nice. If you want to consider the International ranking also IIT Kanpur is above the IIT Roorkee. IIT Kanpur campus is also great.

You can give only JEE Mains 2021, not JEE advance.