It is rather odd and eccentric of her to keep injecting levity into our serious discussions. Hence, 3rd option is the correct choice.
What do you understand by a complete sentence?
A whole sentence has to have a topic and a verb, and the verb needs to be a "finite": A sentence with its primary verb in an '-ing' shape will now no longer be a whole sentence. *
A sentence with its primary verb in an infinitive shape ("to" + verb) will now no longer be a whole sentence.
Hence, It is rather odd and eccentric of her to keep injecting levity into our serious discussions. 3rd option is the correct choice.
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