Fill in the blank with the most appropriate word.
Do you mind ____ the window?
A gerund is a word that is formed with verbs but acts as a noun. Present participles do not act as nouns. A gerund is used as a thing or an idea in a sentence. It also sounds like normal spoken English. Hence, “closing” as given in option A is the correct choice.
Option B has the infinitive form of the verb “to close”, infinitives are used after sentence objects that are nouns or pronouns referring to a person. Here, this is incorrect.
Option C is incorrect as it uses just the verb ‘close’ the window. This is incorrect grammatically.
The combination of the infinitive and the gerund “to closing” is incorrect. It can either be “to close” (infinitive) or (gerund) “closing”. Thus, option D is also incorrect.
Hence, Option A is the correct answer.