When someone is skeptical, that person has many doubts. For instance, we could say, "Although many people are sure that America went to the moon, a small group of skeptical people maintain that this was not the case—in spite of the evidence to the contrary." Such people continually doubt the fact. Thus, among the options provided for this question at least, we could describe them as being "suspicious". While we often call atheists and agnostics "skeptics", this is a particular kind of skepticism, not the more general notion of skepticism as meaning doubting anything.

When someone is a fraud, that person is untruthful about his or her abilities. "Fraudulent" activities are ones that are deceptive. Thus, someone might promise a great return on investments to a group of potential investors knowing that the investment will yield no such return. Such promises are fraudulent. Among the options provided, the best is "deceptive." "Insincere" is tempting, for insincere people are not always truthful; however it is one thing to be insincere by telling someone whom you dislike that you like them. It is another thing altogether to be fraudulent and deceptive in a planned manner. Deception describes active lying; insincerity is more about the manner in which a person behaves, and can be passive, or reflected simply in the manner in which a person interacts with others.

The word "juvenile" comes from the Latin root for young person. Thus, we often use the word "juvenile" to describe someone who is young. When this word is used to describe someone who is a bit older, it takes on the meaning of immature. The implication is that such a juvenile person does not act his or her age. Thus, the best option here is "immature."  While "boyish" might be tempting, this is not a good answer. To be "juvenile" means to be young. While a "boy" may be young, it does not make "boyish" to mean "being young." Of an older person, boyish may be a compliment, while juvenile is almost always a pejorative term for an adult.

The word "regal" comes from the Latin "rex, regis," which means king. Thus, it means king-like. "Regal" can mean either royal or magnificent, depending on the context. Here, the options only provide one acceptable option, namely "royal." The word "regal" is related to other words like "regicide" (the killing of a king) and "regalia" (the emblems used by a monarch).

The word "meticulous" comes from Latin roots that mean fearful. In English, however, this idea of fearfulness has been taken over by the general meaning, attentive to details. (It is as if someone were fearful of missing an important detail.) Now, it could be that such a person is obsessive; however, it is better to say that a meticulous person is diligent. Someone who is careful about details may just be very devoted to making sure that things are done right. Sometimes, this is a very desirable trait. For instance, a meticulous engineer might very carefully design the outer hull of a spaceship.  We would want such a person to be diligent with regard to details and would not want to insult him for being "obsessive." (Of course, diligence can become obsessive.  Still, though, "meticulous" merely denotes being diligent and careful with details, not obsessiveness.) 

When someone is "contemplative," he or she is thoughtful. Often, this is applied to religious people who are engrossed in thoughtful prayer, but it can really describe any kind of thoughtful person. Thus, Socrates was quite contemplative, for a story speaks of how he could stand all night lost in thought. Such a person is best described as "reflective." Though a contemplative person may be likely to be "witty," "genius," or even "forgetful" (at least of day-to-day things), these meanings are not quite right. Above all else, a contemplative person is continuously thoughtful and, hence, "reflective."

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.