I am not sure about the profiles they prefer, but they love engineers i am quite sure of that. The last batch of IIMB (as per their website) said they had 91% engineers!!
I guess having some work-ex would also help, esp in IIMC where they have said that if you have some prior work-ex, it is preferred.
They also have differing requirements for Letters of Reco...IIMA doesnt want one, IIMB wants three, whereas IIMC wants two (preferably from faculties / teachers)
What i did read from another thread on
PG is that the together that three IIMs end up taking like only 4-5 overseas candidates every year - need to check this though.