As you have asked about the Kerala Engineering, Agriculture and Medical (KEAM) entrance exam first allotment date, I am giving you information about it, check below for the details

I want to tell you that the schedule for the allotment for this year has not been released yet.
However, I am giving you information about the last year dates just for reference,

Schedule for First Phase of Allotment:

Date
Events

June 16, 2015
Opening of the online option registration facility

June 22, 2015
Trial Allotment

June 23, 2015– 5 pm
Closing of option registration facility

June 25, 2015
First allotment

June 26, 2015 to July 03, 2015
Candidates allotted to all courses shall have to remit the fee shown in the allotment memo at selected branches of State Bank of Travancore (SBT).
Candidates need not join the colleges after the first allotment

July 1, 2015 onwards
Candidate’s Data Sheet Available Online for Downloading