OSU has won national championships in football seven times the last in 2002. One in baseball in 1966, one in Basketball in 1960, two in golf in 1945 and 1979, five in individual golf, 24 in synchronized swimming, 3 in mens gymnastics, 1 in Track and Field, 11 in mens swimming and diving, 2 in mens fencing, 2 in coed fencing, 3 in womens pistol, 1 in coed pistol, and 1 in Cheerleading.
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The NCAA men's basketball tournament was won by Ohio State University (OSU) in 1960. No other school with the letters "OSU" representing it has won the basketball championship, so if you're referring to Oregon State University or Oklahoma State University or some other OSU, then the answer would be none.