Hello,

You can give IIT JAM for Msc in Mathematics. Basically, a student from BSc does Master i.e. MSc. A student who has done BTech does masters which is MTech. That will increase your skill set and career option.

It is true that you have studied maths for 1.5 years but there is high difference between BSc(Maths) and BTech(Mechanical).  BSc(Maths) students have studied maths for all 3 years and it is highly deep and highly domain focused.

Decide and prepare. see all the aspects. Prepare for the negative side also. MSc in maths is not easy like Btech so if you want to pursue it then you have  very work hard.

Hope it helps!