哪 na3 ‘which’ is an interrogative determinative. When the DET position is occupied with 哪, the noun phrase refers a subset to be identified from a known set, as illustrated below,
你借了哪几本书？
ni3 jie4 le0 na3 ji3 ben3 shu1
you borrow LE which several CL book
‘Which books did you borrow?’
哪in DET potentially has another distinctive reading. It is similar to the existential quantifier 任何 ren4he2 ‘any’ in DET, or falls under the scope of the inclusive adverb 都 dou1 ‘all’, or a negatively oriented polarity-sensitive one in a non-affirmative context, as shown below,
您要见哪位老师吗？
nin2 yao4 jian4 na3 wei4 lao3shi1 ma0
you want see which CL teacher MA
‘Do you want to see any teacher?’
她哪种裙子都敢穿。
ta1 na3 zhong3 qun2zi0 dou1 gan3 chuan1
she which CL skirt all dare wear
‘She dares to wear any kind of skirt.’
不管你去哪里，都不能忘了我。
bu4guan3 ni3 qu4 na3li3 dou1 bu4neng2 wang4 le0 wo3
no_matter you go where all cannot forget LE I
‘No matter where you go, don’t forget me.’
Reference:
Shi, Dingxu. 2016. Nouns and nominal phrases. In A Reference Grammar of Chinese, eds. by Chu-Ren Huang and Dingxu Shi. Cambridge University Press.
