The correct option to complete the sentence is: neither.

"Neither" is used when referring to two entities and implies that not one of them possesses the key. In this case, Mohit and you are the two entities, making "neither" the appropriate choice.

• "None" refers to a non-specific group of three or more entities. Since only Mohit and you are mentioned, "none" wouldn't be accurate.
• "Any" implies that at least one person has a key, which contradicts the statement that nobody did.
• "Either" could be used if the sentence structure focused on the possibility of one of you having a key. However, the sentence emphasizes the lack of keys, making "neither" more apt.