Hi,

No, KLEEE 2021 phase 2 examination has not yet taken pace. The examination will be held from 27th to 29th May 2021. while the registration for the same are still going on and is available till 20th May 2021. The admit cards will be available between May 23 and 24, 2021.The KLEEE application 2021 is available in both online and offline modes. Candidates are required to submit the same before last date depending upon the phase they wish to appear for.

You can refer to this link for more details: https://engineering.careers360.com/articles/kleee#KLEEE-Important-Dates-2021

I hope this helped you.