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Yes.
Yes; in 1950, under Paul "Bear" Bryant, the Wildcats defeated Oklahoma for a national championship in the Sugar Bowl. Note that this was in the pre-BCS era, therefore winners of bowl games were dubbed "National Champions"
Kentucky has defeated Tennessee 144 times out of 210 games played, including a 32-1 (won 20 in a row) record from 1945-1960 (February). In addition, Kentucky was the first program to win 1,000 games after a victory in Knoxville over the Vols on January 18, 1969. Kentucky is 144-66 against the Volunteers. Works Cited; see related link.
the Arizona wildcats have beaten asu 30 straght
If you count UNC and Memphis in the Final Four in 2008.
Through the 2008 season, Kentucky and Florida have met 59 times in football with Kentucky winning 17 times and Florida winning 42 times. The last time Kentucky beat Florida was November 15, 1986 in Lexington by the score of 10-3. Florida has won the last 22 meetings and 28 of the last 29.
From the info I was able to gather, it looks like a tie between Temple and PIttsburgh
OSU has beaten OU 16 times in the Bedlam Rivarly, 8 of the times were in Norman. OU has won beaten OSU 79 times
The University of Kentucky has never been a 'recognized' national champion however they were selected as national champions in 1950 by the Sagarin Ratings and Bill Libby polls. They went 11-1 in 1950 under head coach Bear Bryant and defeated Oklahoma in the Sugar Bowl. Their only loss that season was to Tennessee who was named the national champion.
On March 6, 1962 Wilt Chamberlain scored 100 points in one game. No one has ever beaten that.
Texas A&M has played the University of Texas in football 117 times. The Aggies have won 37 of those, with the most recent win occurring in the 2010 season.
the (4) seed Arizona Wildcats in 1997, Defeated (1) seed Kansas Jayhawks (favored to win it all) in the sweet sixteen: final score 85-82 Defeated (1) seed North Carolina Tar Heels in the final four: final score 66-58 Defeated (1) seed Kentucky Wildcats in the National Championship: final score 84-79