Option C: The given sentence talks about, whether or not there is a way to get inside the house without a key.
Thus, “no” makes sense since then the sentence would mean that "There is no way of getting inside the house without a key" or in other words, “The only way to get inside the house is with a key.”. Hence, this is the correct option.
Option A: “knew” is the simple past tense of “know”. It means having had the knowledge of something beforehand. It is irrelevant in the given sentence. Hence, this option is incorrect.
Option B: “know” refers to having the knowledge of something. It is irrelevant in the given sentence. Hence, this option is incorrect.
Option D: “nod” refers to the act of bobbing the head up and down to show agreement. It is irrelevant in the given sentence. Hence, this option is incorrect.