Former secretary of state Condoleezza Rice thinks Randy Jackson is top dawg!

When the classically trained pianist, 54, was in L.A. for her March 24 appearance on The Tonight Show With Jay Leno, she arranged to meet the American Idol judge, 52, for a private sit-down at the Beverly Wilshire hotel.

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Rice's spokesman tells the new issue of Us Weekly (on newsstands today): "She's a longtime admirer of Randy and enjoyed the opportunity to meet him in person and talk about their common passion for music."

When Jackson (who's been married since 1995) learned Rice wanted to meet him, "he was sort of mystified," a source tells Us, "but he went."

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And they had plenty to talk about during their 90-minute meeting.

Says an insider, "She found him to be absolutely intriguing."

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