I am trying to find out when full synchronization of user profile service was done.
Is there any way to find its last date and time?
You can get a report of the timer job which drives this is called "User Profile Service - User Profile to SharePoint Full Synchronization."
If you go to Central Admin, select Monitoring -> Review Job Definitions, then Job History from the left nav. Change your view to Job Definition, then select the above job from the Job Definition menu. This will show you the last time the job ran.