The prefix inter- means between and the suffix -sect means cut. So, to "intersect" is to cut in the middle of something, to make a cut between two things. This is closest in meaning to "divide" which means to split, to cut in half. Additionally, "outlaw" means ban, forbid; "replenish" means refill, fill something up; "remain" means stay; "outline" means give a summary of something, show the main points. 

The word "inspect" is related to words like "spectator" and "spectacles."  A "spectator" is someone who watches something (like a football game), and "spectacles" are glasses that we use to help our vision. The root "spect-" often has this sense of meaning to look at. Thus, to "in+spect" means to look into something. It means that you look into the details carefully. This is best expressed by "investigate."

The word "verify" comes from the Latin for true. The word "very" means truly, and the "verdict" in a court case is the statement of truth (at least how it is judged to be true). Thus, to "verify" means to prove to be true. The best option given in this question is to confirm. When something is "confirmed," we know that it is the case. (Indeed, the word itself helps to express this sort of meaning—it proves that something is firm or certain.)

The options given for this question are all verbs. When someone "wonders" at something, he or she is amazed by it. For example, we could say, "He wondered at the beauty of the sunset." This means that he was amazed by it. Amazement can also be called admiration. Indeed, the word "admire" comes from the same roots as the word "miracle", meaning something wonderful. Thus we can "admire" something in the same way that we can "wonder" at it.

When something is 'regular," it is said to follow the rule or pattern (The word comes from the Latin regula, meaning rule or measure.) When something is "regulated", it has laws and rules applied to it. "Regular" things do not change much. An "irregular" person does all sorts of crazy things, always unexpectedly. A "regular" person is consistent.

The word "invigorating" really is made up of two parts. The first is the prefix "in-", which here has the obvious meaning of in or into. The second half of the word comes from roots meaning life or lively. Whenever someone or something is "vigorous", it is full of life. Thus, whenever we find something to be "invigorating", it puts life into us. This means that it energizes us and makes us feel alive. Thus, when someone goes skiing very quickly down a mountain slope, this experience can be very refreshing or invigorating.

The word "spectacular" comes from Latin roots that mean to look at. A "spectacle" is something that we watch because it is amazing. Also, we call glasses "spectacles" because we look through them. A "spectator" is someone who watches something. Therefore, when something is "spectacular," it is so amazing that it draws a lot of attention. Such a thing is not merely "interesting" or "important." It is "remarkable" and amazing. Hence, the best option is "remarkable."

The word "industry" describes a particular kind of business. Traditionally, the word described manufacturing processes and businesses. Thus, the "automotive industry" physically made cars, and the "steel industry" took raw material an changed it into steel; however, the word has come to be applied to almost any kind of particular work. The adjective "industrious" describes someone who is hard-working. You can see how this is related to the various kinds of work to which "industry" applies. The only option that describes this sort of hard working person is "diligent." Someone who is "diligent" is devoted and hard-working for a particular task.

To understand this word, it is helpful to consider a word like "grateful." We are grateful for things that are pleasing to us. To be "grateful" is to be thankful for such pleasing things. The adjective "gratifying" means something akin to able to make someone grateful or thankful. Another way to put this is "pleasing," which is the best option among those provided here.

The word "terrain" is related to Latin roots meaning land or physical location. (For instance, think of the word "territory.") Now, the word "battlefield" might tempt you because we use the word "terrain" often when talking about warfare. Also, the word "mountain" is tempting, as it is a kind of terrain. However, the only word that simply means "land" is "ground". Think of when you say "the school's grounds." The word "ground" can refer in general to physical terrain. It is in this sense that it is an acceptable synonym.