The Big Bang Theory Season 6 Episode 20
The Tenure Turbulence
When a tenured professor dies, the guys are pitted against each other for the open position. Mrs Davis from the Human Resources department is on the committee and Sheldon previously had a run in with her over his treatment of his assistant.
Leonard goes to the gym to work out when she's there and nearly dies from the strenuous activity. Sheldon buys her an inappropriate gift: Roots DVD. And, Raj sends her a 90-minute video about himself. Meanwhile, Kripke works out with her regularly and even offers to babysit her kids.
They all say they aren't going to the funeral, but end up going when they hear the tenure committee with be there. Sheldon takes Amy with him for support. Leonard takes Penny to wow the committee with her very sexy dress. And, Raj, Howard, and Bernadette show up as well.
In the end, Sheldon, Leonard, and Raj are all put on the short list for the tenured position.