The winner of the Rangers v Albion Rovers quarter-final replay will face Dundee United in the semi-final of the Scottish Cup.
And St Johnstone will face Aberdeen in their semi-final match, just as they did in the Scottish League Cup.
Aberdeen won that clash at Tynecastle in January to set up a final next Sunday against Inverness, who missed out on the Scottish Cup's last four after defeat to Dundee United.
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The draw was made by Winter Olympic curling silver-medallist Greg Drummond and Brian McColgan from competition sponsors William Hill.
The ties will be played on the weekend of April 12 and 13 at Ibrox Stadium.