All five words are adjectives that describe a person's ability. "Inept" means incompetent, or unskilled. The "inept" teacher might routinely lose her students' papers. "Competent," "proficient," "skilled," and "qualified" are all synonyms meaning capable, or able to complete the assigned tasks. These words are all antonyms of "inept." 

When someone is “indolent,” he or she is lazy. The word “dolor” means “sadness or distress,” and “indolent” literally means “wishing to avoid any distress (hence, any work).” The other options all indicate personality aspects that are full of energy. The only word among them that might be a bit unknown is “vigorous,” which means “healthy and full of energy or strength.”

"Car", "plane", and "train" all describe different modes of transportation.  "Fly" describes a method of transportation, and would belong with "drive" or "run" or "walk".

Notice that each of the similar words pertains to something brief, immediate, or short-lived. Probably the only word that is a bit out of the ordinary among those provided is “blitz.” If you are an American football fan, you will know this word, but the original meaning (which is related) antedates the sport. It means “a quick and / or sudden attack.” The word is sometimes applied to the game of chess when moves must be made very quickly in sequence with little time between them. Something “prolonged” is neither blitz-like nor immediate (or any of the other related words).

All of the related words pertain to the state of being underfed or lacking food. To be famished is to be in a state of extreme hunger, and to be “malnourished” is to lack appropriate nutrients, either because lack of diet or at least lack of appropriate food intake. While someone who is starving is in a state of extremity—great difficulty and suffering—the word “extremity” can be applied to many other things than starving.

All of the “related” words appear to be rather unrelated. This mutual opposition should be a key, however. Note that regularity / irregularity as well as uniformity and being erratic all pertain to how some activity matches a pattern (or does not do so). The case of “schedule” merely describes a potential pattern. It is not an evaluation of the following thereof.

You may well have gotten this question correct because “psychological” appears quite less harmful than any of the other options listed; however, this is not the proper reason for that word not “fitting” with the others. Instead, each of these listed maladies are types of psychological disturbances. In distinction to this grouping, the word “psychological” is a broad category into which the others could be placed. It thus differs qualitatively from the other options.

Each of the related words pertains to deep thought. A contemplative person is someone gives deep thought to matters. He or she might also be someone who is prayerful, but the word is used in this latter sense because it indicates a recollected state of thoughtfulness. The word “cogitation” is related to “recognize,” which literally means “to know again.” Cogitation is deep thought about something. To be “pensive” is to be reflective in temperament. It is related to the Latin word for “to weigh,” which is found in English words like “compensate” and “expensive.” When we compensate someone, we weight out how much they should receive in payment. Only the word religious does not necessarily indicate contemplativeness. This is not meant as an insult to religion, but is merely an observation that many can be called “religious” but not have a contemplative personality. Such persons can often do great charitable deeds, but this is not the same as being contemplative or pensive. This could or could not be the case, depending on the religious person in question.

All of the related words for this question pertain to leading or guiding. Likely the most troublesome word in this group is “conduct”—if you read it as being “somebody’s manner of acting;” however, remember that “conduct” can also mean “to lead” (as in a “conductor” who directs a train on its way or an orchestral conductor who leads an orchestra). Only “behavior” does not fit this group, for it is far too broad and does not signify leading in any explicit manner.

The set of related words all indicate something that pertains to someone’s energy level. A sluggish or languid person is slow and lacks energy. In contrast, someone who is “ebullient” is full or energy (and perhaps cheerful in a “bubbly” way). A vibrant personality is one that is enthusiastic and energetic. To speak of “concentration” does not necessarily indicate anything (one way or the other) pertaining to energy. It is therefore the word that is not related to the others.