Inverness await the winners of the Old Firm Scottish Cup replay after Sunday's quarter-final draw.
Rangers and Celtic drew 2-2 in a tempestuous fifth-round encounter at Ibrox, where the draw was then conducted - with a trip to Tulloch Caledonian Stadium awaiting the winners of the return match at Parkhead.
Holders Dundee United were the first team drawn and host Clydesdale Bank Premier League rivals Motherwell.
St Mirren host the winners of Sunday afternoon's tie between Aberdeen and Dunfermline while Division Two side Brechin's reward for beating minnows Buckie Thistle is a home game against St Johnstone or Partick Thistle, whose match in Perth was postponed until Tuesday night due to a waterlogged pitch.
Ties will be played on the weekend of March 12 and 13.
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