A fragment is described as a detached group of words, phrases, or clauses proposing an incomplete meaning. These are often called broken or shattered parts(lacking an accomplished meaning due to the absence of either the verb or subject) that might have been separated from a sentence.
As per the question, option A i.e. 'To prepare for the 10K race' exemplify a fragment as it lacks a subject and main verb and proposes an incomplete meaning. Since it offers an incomplete thought and does not possess the ability to stand on its own, it demonstrates a fragment. It could propose an accomplished thought only when either it is added to a sentence or rectified by placing an appropriate subject and verb in it. Thus, <u>option A</u> is the correct answer.
This question lacks context but I will try to answer with what I can. When a poem juxtaposes, it places two different things side by side so you can compare and contrast, giving the poem an interesting effect. The poem might be suggesting that there are many similarities in the two subjects being juxtaposed as well as differences.