Depends.
Usually won.
The thread title says its queen and rook vs queen not queen and rook vs rook and certainly not queen vs rook.
Should be won, even with Black to play. If White plays accurately he should probably be able to avoid perpetual I would imagine.
Well in most positions, Q+Q vs Q is drawn so I could only imagine that unless black places his queen poorly, then it should be drawn.
If there are pawns on the board it would make it much easier to win because the king can use them for shelter.
2Q vs. Q I would guess is almost always, if not always, winning no matter which side is to move.
Before black played Qc6+?, it was a draw in the example above. Even after black played Qc6+?, it is practically very challenging to win this endgame (if black defends properly, which is challenging to do). White has to find some only moves to win. But, the win is much easier if the superior side has pawns.
Queen and Rook would win because -
Queen and Rook would win because -
On move seven white could just check on f2 and force an exchange of queens and mate with rook and king.
Queen and Rook would win because -
On move seven white could just check on f2 and force an exchange of queens and mate with rook and king.
I knew, but I am not that advanced to mate with a rook and king vs king.
Win or draw?