Answer:
The correct answer is - Nodding, Mom said she would rather be early than late.
Step-by-step explanation:
Present participle verbal looks like a regular verb + -ing (singing, dancing, sleeping, etc) and has the function of either adjectives or adverbs within a sentence.
If you're unsure about the correct answer, let's use the system of elimination:
A is incorrect because there is no participle here at all. There is a verbal to leave, but it is an infinitive, not a participle.
B is incorrect because, again, there is no participle here, only infinitive to go.
C is also incorrect because, even though there is a verb + -ing form in the sentence (the word leaving), it is not a participle, but rather a gerund (gerunds are used as nouns).
Therefore, the only correct option would be sentence D, where the present participle nodding is used as an adjective to describe Mom.