Choose the correct particle

1. Can you help me pick [up|out] a nice dress to wear tonight?
2. She kept [up|on] working even though she was tired.
3. Jane was let [down|out] of the hospital yesterday.
4. Some of the children were teasing and picking [on|out] Bill.
5. If you don't come, you'll be letting me [down|out].
6. Most film stars have bodyguards to keep [from|away] fans.