If you are strong in Maths and Physics means..... Better Choose EEE.....
Well as you are weak in drawing then mechanical stream will not suit you at all.But in ECE/EEE/CSE/IT all have good scope for you.But according to me ECE is best option for you as if you are interested in research then it will suit you as you can do your doctorate in ECE after your M.Tech.
Join MECH the ever green branch buddy go for it..
Don't think much the best one is this.
ECE is the best ever carrier oriented course.
when it comes to EEE/ECE both will have 60% of subjects in common because ECE is a sub-branch which is derived from EEE. Mechanical engineering mainly deals with machine design, mechanics and there will be lot of engineering drawing you come across in most of the semesters.
ECE n EEE will be grt options fr you....neat work and gud research scope.even Comp. Sc. is gud.
ECE/EEE are not good but these branches are not best now because of lot of student in these lines.
similar to mechanical but still lot's of job available for mechanical profession.
as u said u want to do research work. mechanical is perfect like engines,cars.machines,generators.. etc .
so according u should go for mecahnical..
but if u have intrest Electrical then go for Pure Electrical Branch(not ei,eee etc..)
main advantage in pure electrical is that very less seat are available's and very less students..
still minimum faculty in pure electrical.
u can join various research institute or organization like drdo,cbri,atomic centres etc...
SO MECAHNICAL/PURE ELECTRICAL IS PERFECT.