JEE is Joint Entrance exam for admission to UG Engineering Programs at NITs, IIITs, Other Centrally Funded Technical Institutions, Institutions funded by participating State Governments, and other Institutions.

As you have asked about the IIT JEE application form date, check below for the information

The closing date to register for JEE Main 2016 has been extended.
The initially announced last date, to apply, was 31 December 2015 but now it has been extended till 11 January 2016.
Applicants, who are not registered yet, must use this opportunity and apply for JEE Main 2016.

Date of Examination:

JEE(Main)-
Paper-1 (B.E./B. Tech.) [Offline examination]:03.04.2016
JEE(Main)- Paper-1 (B.E./B. Tech.) [Online examination ]: 09,10 April, 2016
JEE(Main)- Paper-2 (B.Arch./B.Planning) [Offline examination]:03.04.2016

JEE Main 2016 Application Form – Prerequisites
Before filling the application form of JEE, do keep the following ready:
Valid E-mail ID and Phone Number
Documents of the Qualifying Examination, if issued
Debit/Credit Card, e-Challan details, for fee payment
Scanned Photograph, Signature and Thumb Impression
A Password, which applicants would like to use for their login

You can fill application form by logging in to the JEE main website.

Contact Information:
JEE(Main) Unit Central Board of Secondary Education
Plot No. 149, Block - H,
Sector - 63, Noida - 201309
Distt- Gautam Budh Nagar (U.P.)
Helpline No.
7042399520, 7042399521, 7042399524, 7042399525, 7042399526, 7042399528,7042399529
Computer Based Exam Helpline No.
18002660372 (only during 15th March - 15th April 2016)