Question on Managed Properties

1. In SharePoint 2010, if I create a managed metadata column... does it automatically become a managed property in FAST Search engine?
2. In SharePoint 2010, if I create a site column... does it automatically become a managed property in FAST Search engine?
3. In SharePoint 2013, if I create a managed metadata column..does it automatically become a managed property in the SP2013 Search Engine?
4. In SharePoint 2010, if I create a site column... does it automatically become a managed property in SP2013 Search Engine?

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