After defeating Bowser, you can find Mayor Pauline waiting for you in front of Town Hall in New Donk City. If you talk to her, she will have quiz questions to learn more about her.
These questions include things like “What is my most treasured possession?” and “What do I plan to eat for dinner tonight?”. They appear in a random order, making it difficult to memorize the answers.
What are the answers to Mayor Pauline’s quiz questions?
Best Answer
Question: How am I doing as mayor of this city?
Answer: Fantastic!
Question: What is my most treasured possession?
Answer: A hat.
Question: What kind of music do I like?
Answer: Peppy music.
Question: What am I bad with?
Answer: Fixing machines.
Question: What do I just adore?
Answer: Cake.
Question: What do you think my hobby is?
Answer: Going on walks.
Question: Which of these things did I actually do a long time ago?1
Answer: Captured by ape.
Question: What do I plan to eat for dinner tonight?
Answer: Fried mushrooms.
Credit to @Bing for the following:
Question: What do I do on my days off?
Answer: Practice singing.
Sources: this YouTube video and article
1 I don't know if there is basis for the rest of these questions and whether answers are found in game or not (presumably not), but this one stems from Pauline being the girl captured by Donkey Kong in the original Donkey Kong.