“Torrid” means stiflingly hot and sweltering when describing the weather or a climate, very difficult, or passionate when describing a relationship. "Sweltering" is thus the correct answer. As for the other answer choices, “freezing” means very cold; “blustery” means windy; “moist” means damp or a little wet; and “precipitous” means sheer or intensely steep.

“Obscure” means hidden or esoteric, so "hidden" is the correct answer. Something that is “obvious” is easy to know and understand; “coherent” means able to be understood; “abrupt” means happening quickly and suddenly without any forewarning; and “acceptable” means good enough.

Perhaps you have heard of "ductility" in your science class. This is a property of metal that describes its ability to be made into a wire. For something to be "ductile" (and hence formed into a wire), it must be flexible. Otherwise, it would break. Do not choose "ventilated" (as though the word "ductile" was related to "air ducts"). Likewise, don't choose "wired!" Something that is ductile can be made into a wire; however, it certainly is not itself "wired."

The word "radiant" comes from Latin roots that mean to send out rays. Think of X-rays. Such technology is so named precisely because these devices use waves or "rays" to detect bone (and other) structures in your body. There can be "rays of sun," meaning the sunlight itself, shining. Thus, when we say that something is "radiant," we mean that it is shining. This word can be used metaphorically meaning joyful, as we say something like, "He was radiant when his mother told him that he would have his favorite dessert that that night."

For this word, be careful not to be fooled! There are a number of options that are meant to fool you into choosing a word that is only close but not exact. When things are "identical," they are exactly the same. Thus, it is not fair to say that they are merely similar, akin, or alike. All of those options merely mean that the things in question are nearly the same but not quite. Thus, the best option is "duplicate."  duplicate is a double of something else. It is an exact copy. Thus, this option is far better than the other ones offered!

"Covert" is an adjective describing something that is secret, hidden, or undercover. "Open" can be an antonym to "covert" if used to describe someone's attitude towards information. None of the other words are particularly related to "covert."

Counterfeit is an adjective describing something that is fake, fraudulent, or unreal. "Counter-" is a prefix that connotes an opposite. "Valid" is close to an antonym to counterfeit.

"Noxious" means harmful or poisonous. A "noxious" gas might be toxic. "Hateful" means either deserving of or being filled with extreme anger. "Disruptive" means tending to disturb the normal order of a situation. "Exposed" refers to being uncovered or made visible.

The word "vacant" is related to the words "vacuum" and "vacation." A "vacuum" is an empty space. A vacation is "empty time" during which you can rest and do what you want to do. Whenever a piece of property is "vacant," it is empty, having nobody occupying it. We can also use the word "vacant" to describe something that is generally empty. Thus, a "vacant stare" is a facial expression that is "empty"—as though the person were looking off into space without any particular focus.

Whenever something is "stately," it is majestic or very grand. Things that are "important" can also be called "stately," but the two words are not exact synonyms. Instead, the best option for this question is the simple "impressive." Whenever something is "stately," its majesty and grandeur are impressive.