The word "equivalent" has a base that is certainly quite familiar to you: "equ-" as used in "equal," "equally," and so forth. When two things are "equivalent," they are the same, like 2 and 1 + 1.  Equivalence indicates a greater degree of correspondence than mere similarity. Two people might be similar in appearance, but equivalence is strict equality. Therefore, the best option among those given is "identical," which indicates such strict equivalence.

"Bizarre" means strange or unusual. This word is often used to describe appearances. "Common" and "familiar," which mean usual or encountered often, refer to things that you see often or have seen before, and are opposites of the answer we want. Finally, "crowded" might be used to describe an event packed with lots of people.

"Detrimental" means likely to cause injury or damage; therefore, "damaging" is the word that most closely matches the definition of "detrimental." "Liberating," which means freeing, and "seldom," which means rarely, are unrelated to the definition, as is "possessively."

"Despicable" means to be loathsome, or deserving of hate. The word that most closely takes on this meaning is "terrible," which is something that is very bad. While both "ugly" (repulsive-looking) and "terrible" are negative terms, something that is "ugly" is not necessarily "despicable." Similarly, something that is "dark" or "serious" would also not be "despicable."

Something that is "derogatory" is disrespectful and offensive to another person. Something that is "insulting" puts down another person. Given how similar these meanings are, these words are synonyms.

For this question, you just need to be careful about the intensity of the word. Something that is "frigid" is very cold. Therefore, the best option is "freezing", for this word describes the coldest condition among the options given to you. Always find the word that is closest to the intensity indicated by your word.

The word "metropolitan" means related to a city, of the city. To provide further help, "rural" means away from the city, farmland. "Beach" is an area of land overlooking an ocean. "Cancer" and "creation" are both unrelated.

The word "summit" does not have to do with mathematical "sums"—as in addition! Instead, the word means the highest point. Therefore, we talk about the "summit of the mountain", meaning by this the highest point on the mountain.  This is the same as the "peak" of the mountain.

The word "minor" comes from the Latin for less. It is the opposite of "major," which comes from the Latin meaning more. A "minor" concern is a concern that is not very important. Among the options provided, the only one that expresses this sort of lack of importance is "unimportant." You could use this word in a sentence like, "That was a minor insult, so I am not too sad." This means that it was a small insult; hence, it was not very hurtful.

The word "oblivious" is used to describe someone who is totally unaware of some set of facts. For example, we could say, "Steven was working so diligently on his homework that he was utterly oblivious to the loud sounds outside of his bedroom." This means that he was totally unaware of them, not even hearing them!