1) ONE OF THE X'S THAT/WHO<PLURAL>
2) ONE OF THE X'S <SINGULAR>
3)ONLY ONE OF THE X'S <SINGULAR>
4)ONLY ONE OF THE X'S THAT/WHO <PLURAL>
5) "THE" ONLY ONE OF THE X'S<SINGULAR>

Source: https://www.beatthegmat.com/one-of-the-t40356.html

regards,
Patanjali

19. Every workday at dawn, the patriarch of one of the city's five richest families leaves his mansion and walks to city hall.
a) richest families leaves his mansion and walks
b) richest families leave his mansion and walk
c) richest families leaves his mansion and walk
d) richer families leave his mansion and walks
e) richer families leaves his mansion and walks

Good question - and with a question like this it's often quite a bit easier to just think logically about who is performing the action: is it one person (singular) or several (plural)?

As bubbliiiiii noted, it's the patriarch. If it weren't him:

1) "The patriarch" then wouldn't have a real purpose in the sentence
2) You wouldn't use "his mansion"

Quite a few S/V Agreement questions can be solved just thinking logically about who really "does" the verb, and the great thing about thinking that way is that it's scalable - you can always think logically whereas relying on memorized rules is tough. If you're in doubt and find yourself entrenched in a grammar battle, take a step backward and see if you can fight the logical battle instead. Usually that gets it done...