Topic: Right Form of Verb,

Best Answer Explained in Below-:

The sentence "Would you mind — the window." requires a gerund, which is the -ing form of a verb, to complete it correctly. In English, the phrase "would you mind" is commonly followed by a gerund when expressing a polite request. This structure essentially asks for permission for someone to perform an action, indicating that it may cause a slight inconvenience.

In this case, "opening" effectively fills the blank: "Would you mind opening the window?" This construction is both polite and grammatically correct.

Looking at the other options, "open" (A) is the base form of the verb and does not fit the structure following "mind." "Have opened" (C) indicates a completed action in the past, which does not match the request being made. "To open" (D) is an infinitive form and is also not used with "mind" in this context. Thus, the correct answer is B) opening, as it correctly transforms the verb into a form that aligns with the expectations of English grammar in polite requests.