would you mind _____the door?

C
常用用法有:
1. Would you mind + 名词宾格/形容词性物主代词 + doing.
例：Would you mind me/my smoking here?
你介意我在这里抽烟吗？
Would you mind me/my opening the window?
你介意我开窗户吗？
2.Would you mind + if 从句。
例：Would you mind if I smoke?
你介意我抽烟吗？
Would you mind if I were to say...
我这样说的话，你介意吗？

Would you mind 句型一般用在面对陌生人时或者非常正式的场合，用来表达委婉、客气的意愿，不用在朋友之间，或者普通、随便的场合。
……

Yes, I'd love to.
Yes, please.
No, thank you.
Sorry, I'm afraid not.

C
已经有主语you了所以要用宾语me.

mind + doing 固定用法

c

c
would sb mind (sb) doing sth
eg:would you mind me smoking here? OR would you mind my smoking here?
回答一般是： yes, i do mind.
no of course not.

C
mind的用法是这样的：mind (sb/one's) doing sth
其中mind one's doing 比 mind sb doing 更婉转一些
所以答案只能是C

C