Yes, if the below questions are answered, Facebook might appoint you in the appropriate fields mentioned.
(For Product designer job)
If you are fed up with the ATM machines and decides to design a new one, how would you do it?
(For Data scientist job)
If a day is given, how many birthday posts would come?
(For Technical project manager job)
How does the website work?
(For Risk analyst job)
How many Vacuum cleaners are there in USA?
(For Operations associate user intelligence)
While uploading a photo on FB, if it's dropped by 50%, what would you do?
(For Media solutions specialist job)
What is that which least bothers you in your resume?
(For User Operations analyst)
How do you identify a fake profile on FB?
(For Account manager job)
How much money is spent on the internet?
By Phani