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Holders Arsenal will face Sunderland at home in the third round of the FA Cup.
The two sides met in the Barclays Premier League at the Emirates Stadium on Saturday, with the Gunners recording a 3-1 victory.
If part-timers Whitehawk come through their replay against Dagenham & Redbridge, their third-round debut will see them face top-flight opposition in Everton at Goodison Park.
Sixth-tier Whitehawk were one of four non-league teams to feature in the draw made in Cardiff on Monday night.
The lowest-ranked among them, Salford City, will host Sky Bet Championship Derby if the seventh-tier club get past Hartlepool in their second-round replay.
Eastleigh, the only one of the quartet to have made it through outright, were handed a home tie against Championship basement boys Bolton, while the draw also pitted the winner of Grimsby's second-round clash against Shrewsbury - being played on Monday night - to face Cardiff away.