I may get Mech @IITHYD and Metallurgy @IITB.My interest lies in Robotics. Is it worth taking Mech @IITHydvis a visthe opporunities and exposure at IITB?

definitely metallurgy has negligible connection to robotics. you will get opportunities at iitbombay but if robotics is your passion for life, then why compromise?go for mech at iith if you like mech so much. if robotics is a hobby, and you wont get bogged down or irritated by the amount of mugging up you have to do in meta, then go for bombay. there may be intermediate choices also available in other institutes so please check them out as well. try for electrical or electronics somewhere.

all the best