The word "resolute" comes from similar roots as "resolve" and "resolution." These words mean in general to come to a determined decision. The particular adjective "resolute" describes someone who has decided in a fixed and unchanging manner. Thus, the best answer is "steadfast," which describes someone in a similar manner.

When someone is "precise," he or she is exact about details. Now, this can be used to mean that the person is not vague (in speech, writing, etc). It can also mean that the person is very exacting about details when working. Such a person is well described as being "methodical." This word describes someone who works on something by using a fixed method. This allows him or her to address all needed details for the given matter (instead of randomly working on it and, thus, missing important details).

You might think that the adjective "pretentious" describes someone who is arrogant; however, this is not exactly correct. A person is pretentious when he or she acts like he or she is better than he or she is in reality. Thus, the simple word "showy" is the best option among those proposed here.

We tend to think of "partial" as being contrasted to "whole." In a way, this does apply to the meaning needed for this question but not entirely. Someone can be called "partial" when he or she favors one thing over another. Thus, you could say, "I am partial for the thought of Roger Kilwardby," meaning that I favor his way of thinking about things. Sometimes, we speak of "showing partiality"—this means showing a kind of favoritism. Now, these cases are like taking a "part" (e.g. Roger Kilwardby) at the expense of all other people or things. This could be called having a prejudice (at least in a mild form). Thus, this is the correct answer.

There are two classes of wrong answers for this question. One set is trying to get you to misread "insolent" to be "insolvent." When you are "insolvent", you are bankrupt, but this is totally wrong, for the word is insolent! Now, the word "insolent" means rude. You might know an expression like "insolent brat" or "insolent fool." Thus, you would know at least that insolence is a bad character trait, but do not go from this general feeling to the conclusion that options like "manipulative" or "conniving" are correct. (These are the second set of trap answers.) Instead, "uncivil" is the best, for it is closest in meaning to "rude."

The word "meticulous" describes someone who is very careful about details. The best option among those provided is "fastidious," which means nearly the same thing. For a pairing like this, it is just necessary to know the vocabulary words in order to answer the question correctly.

As you well know, the word "devoted" means loyal, but the options for answers given here might make you worry about this initial thought. You might think that the word has religious overtones, for related words like "devotional" and "devotions" are sometimes related to religious matters, but this is not the case for any of the main meanings of "devoted" (though it certainly is related historically to those other meanings). Now, the word "staunch" actually does mean "loyal." Just think about a somewhat familiar way of speaking: "He was a staunch defender of the new legislation." This means that he was a loyal or devoted defender of the legislation. Thus, "staunch" is the synonym needed for this question.

The word "zealous" and "zeal" come from Latin roots that mean jealous. To be "zealous" is to be energetic with regard to something. It is a kind of "jealous anger" or "jealous energy"—not so much in the sense of being envious as in the sense of desiring something intensely. Thus, a zealous person is very devoted to his or her cause and could rightly be described as being "committed," which is the best option among those provided. 

The word "pensive" is related to the French "penser," as in the famous expression of Descartes: "Je pense donc je suis!"—"I think therefore I am!" Someone who is "pensive" is reflective and thoughtful. This does not mean that the person is necessarily deeply wise or intelligent (though this may quite well be the case). To be pensive means that you can ponder. Among the options, the best is "introspective." This means inward looking (=intro + spective). A person who is thoughtful, looks inward (so to speak) and reflects for a long time.

When someone is "diligent," he or she is devoted to his or her work. Now, while this would likely make you think that "devoted" would be the best option, actually "industrious" is slightly better. When someone is "industrious," he or she is works with great care and devotion. This expresses the role of work in the devotion better than the simple word "devoted."