1) Have you stolen more than four hundred dollars in cash or property from an employer?
2) Are you withholding information regarding your illegal drug history?
3) Have you committed an undisclosed serious crime?
4) Based on your personal bias, have you ever committed a negative act against anyone?
5) During a domestic dispute, have you physically harmed a significant other?
For the most part, these are very obvious relevant questions. But note that #4 is vague enough that it might easily be confused for a probable-lie "control" question.
Commonly used "control" questions include:
1) Prior to your application, did you ever lie to someone in a position of authority?
2) Before this year, did you ever put false information on an official document?
3) Prior to this year, did you ever betray someone who trusted your word?
4) Before your LAPD application, did you ever do anything that would place your integrity into question?
5) Before this year, did you ever take credit for something you didn't do?
6) Prior to this year, did you ever deceive a family member?