* JEE Main: This is the first stage of the entrance exam. It's a qualifying exam for JEE Advanced.
* JEE Advanced: This is the second stage and is only for students who qualify JEE Main. It's used for admission to the IITs.
So, while there's no single full form encompassing all IIT entrance exams, JEE (Joint Entrance Examination) is the most accurate and widely understood answer.