see 1st u find out abt production engineering what kinda placements etc and ck out the course of mech and placements
then u hv to choose from bitsp and nit trichy -they hv almost same value leave goa so now u hv to worry abt ur branch
i think upgrading ur branch in bits is xtremely tuff u need to top ie cgpa 10 hwever branch upgradation in trichy is more feasable so if u wanna go 4 cse or ece go 4 trichy by upgradation else go 4 bitsp if u like mech