The correct answer is: B. no article, no article
The sentence is about Roger giving a ten dollar note to someone. The ten dollar note is not specific, so it does not need an article.
Option A is incorrect because “a” is used to introduce a specific noun. In this sentence, the ten dollar note is not specific, so “a” is not necessary.
Option C is incorrect because “the” is used to introduce a specific noun that has already been mentioned. In this sentence, the ten dollar note has not been mentioned before, so “the” is not necessary.
Option D is incorrect because “the” is used to introduce a specific noun that is unique or well-known. In this sentence, the ten dollar note is not unique or well-known, so “the” is not necessary.