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Gainsborough Trinity's tie at Harrogate Town and Kettering Town's home match with Doncaster Rovers in the FA Cup second round will be broadcast live on BBC Two.
Seventh-tier Trinity are the lowest-ranked side left in the competition after they beat fellow Northern Premier League team Hednesford Town on penalties in the first round.
Kettering - leaders of the Southern League Premier Division Central - produced the biggest shock of the previous round by defeating League One Northampton Town.
Harrogate host Gainsborough on Friday, 29 November at 19:45 GMT, before Kettering and Doncaster meet on Sunday, 1 December at 12:00.