Government & Defence Entrance Exam

First of all, you need not do B.Tech and M.Tech to join Indian Army as technical officers. You have following options to join Indian Army as a commissioned officer:
(a) Join army through NDA and chose technical corp after completion of training at NDA & IMA. Army educates selected candidates to become mechanical and telecommunication engineer. Selection is based on NDA exam conducted by UPSC after B.Tech/M.Tech.
(b) Join OTS Chennai in 10+2 Technical Direct Entry scheme. This is open for male candidates who have passed 12th Class with physics, chemistry and mathematics with not less than 70%. Those who make it in merit list based on marks undergo SSB for selection. After 5 years at OTS and CME-Pune or MCTE or MCEME Secunderabad, candidates get engineering degree and job with starting salary of CTC of Rs 6+ Lakhs.
(c) University Entry Scheme to join in the final year of B.Tech degree.
It is recommended that you go for option (a) or (b). You will get B.Tech degree from JNU on the expenses of the government of India. Indian Army sponsors engineers for post graduation degree in IITs based on the performance in Army.