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Deleting cards is, unfortunately, a permanent action, and deleted cards are unrecoverable unless you have a backup & recovery Power-Up like Backups for Trello. Without a Power-Up in place, they are permanently deleted.
You can check if the cards were inadvertently only archived, which is recoverable: http://help.trello.com/article/795-archiving-and-deleting-cards
We also have an export feature to export your boards as backups: https://help.trello.com/article/747-exporting-data-from-trello-1
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