hi,

see you may apply in gate exam from electrical engineering branch. any of engineering student can apply for gate exam from any other branches, but as for psu recruitment and drdo you will not eligible to get call from drdo or any other psu as there criteria  for electrical engineering branch recruitment is student need to pass b.tech on electrical or in electrical and electronics or electrical and power engineering.  most of the mechatronics engineers opts gate paper on mechanical engineering as there is some similarity in mechatronics and mechanical engineering syllabus. however even for m.tech admission in iits you will not be eligible for electrical engineering related stream for m.tech admission.