See.. Both branch change and partial drop are tough things. I don't know the scene of IIT BHU.
But in Roorkee, guys from geology or polymer get branch change easily into metallurgy as metallurgy have plenty of seats but in other core branches it again requires above 9 cgpa and available seats.
Branch change is tough as for 1st year courses are common and we have relative marking scheme.
Partial drop can be taken if you remain determined to prepare well and give your 100%. This has lesser risk coz even if you don't get desired branch in IIT next year you will have something by your side.