In IIT i got a rank of 6933 and in aieee i have got a rank of 3526.so will you please tell me that whether -IIT or NIT what should i prefer?If NIT,thenwhich NIT will be the best of all and what branch should i select.

You've got a not so good rank in jee. With this u wud get something in new iit's or a course in dhanbad only. But ur rank in EEE is quite gud .

I Think u should try NIT's , especially Warrangal , Trichy or Motilal nehru (allahabad).