Does the A320 Trimmable Horizontal Stabilizer automatically reset after landing?
If the quiz you saw is the same as this one, then please double-check it, as the one I linked has 'THS only' as the correct answer...


  Q 31: Which of the following will automatically reset after landing?
  A: THS.
  B: Rudder trim.
  C: Both are correct.


... which is more inline with the manual.

THS -- yes

The THS resets to 0° after being on the ground for +5 seconds and with the pitch attitude less than +2.5°. This is when the pitch law reverts to 'ground mode'.


  Ground mode is a direct relationship between sidestick deflection and elevator deflection, without auto trim.
  It automatically sets the trimmable horizontal stabilizer (THS) at 0 ° (inside the green band).
  
  (A320 FCOM)


Also see: Why is it not recommended to hold the nose up on the A320 after touchdown?

Rudder -- no

There is no similar 'ground mode' for the rudder, and the manual does not mention an automatic rudder trim reset as far as I've checked.* I doubt one exists because in an engine-out landing, such reset would catch the pilot off balance. (The SOP calls for 5° trim towards the working engine when landing with an engine out.)

The SOP also calls for checking the rudder trim is zero after start, and resetting it if it is not.



* The manuals do not always tell the full story as Captain Sullenberger learned, so it goes without saying to not use the internet for flight.