IT BHU mechanical or IIIT HYD CSE or NIT TRICHY ?

IIIT HYD is international institute of technology...my IIT JEE AIR is 3458....AIEEE AIR is 1996...on checkin last year's opening and closin ranks...i found the above two courses most appealing to me..and those which i may get..plz help me to decide which one to take..is IT BHU an IIT from now on??...IIT has introduced a third round of counselling too...does the opening and closing ranks differ because of that??