Holders Celtic will face Aberdeen while Rangers take on Heart of Midlothian in the Scottish Cup semi-finals.
Both matches will take place at Hampden Park on the weekend of 20 April.
However, Hearts had coach Steven Naismith retains belief that that they can upset the odds to lift the cup for a ninth time in their history and for the first time since 2012. "We have had a good bit of progression since the last semi-final. We want to progress again and give ourselves a chance to win it.
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