[Serie: All About Japanese Particles]
Note: Men tend to use the forms mono ka and mon ka, women mono desu ka and mon desu ka.
1. Emphasizes a determination not to do something by means of a rhetorical question.
あんな所、もう行くもんか。
Anna tokoro, mō iku mon ka.
I wouldn’t be caught dead going there again.
あんな人一緒に仕事ができるもんですか。
Anna hito to issho ni shigoto da dekiru mon desu ka.
I wouldn’t work with her again if my life depended on it.
– Source: All about particles – A handbook of Japanese function words –