The word "brisk" can refer to cool weather, but it can also be used as an adjective describing fast movement. The adverb "briskly" means quickly or with energy. A brisk motion is one that is fast, and walking briskly means walking quickly with haste. In contrast to this, a leisurely pace is one that is slow—taking its time. Leisure is the free time used for enjoyable activities. Such time is not usually stressful. Therefore, "leisurely" activities are quite slow in their pace.

We are looking for something that simply implies irregularity as opposed to regularity. When something is done inconsistently, it is done without a regular manner or mode. A consistent tempo is one that is regular and repeated. Therefore, "inconsistently" is a good antonym for "regularly."

To be "coarse" means to lack refinement or to be "rough." Indeed, the word first has the physical sense of being rough—like a coarse, rough piece of sandpaper. In contrast to this, something that is delicate is fine in quality. Thus, to do something "delicately" is to do that thing in a way that is opposite to being "coarsely" done.

The adverb "fortunately" describes a circumstance that is positive or happy. To say, "Fortunately, a student raised her hand in response to the question," is like saying, "It is a fortunate and positive thing that a student raised her hand in response to the question." The word "lament" means to wail or otherwise express sadness greatly. When we say that something "lamentably happened," we mean to say that it is unfortunate or sad that it happened. This is quite the opposite of something fortunately happening.

The adjective "cheerful" is, of course, very familiar. It generally is taken to mean "happy." In addition to this basic sense, both the adjective and the adverb "cheerfully" connote a kind of optimism as well—i.e. looking on the "bright side" of things. Pessimism or hopelessness is opposed to such cheerfulness; therefore, the best option among those given is the adverb "hopelessly."

The adverb "generally" can indicate that something happens in a broad, unspecified manner or that something happens in most cases. For instance we could say, "Generally speaking, it is true that scientists are good at math." We contrast such general speaking to being specific or particular. We can likewise contrast it to something that does not happen usually—i.e. something that happens rarely. For instance, "Generally, it does not rain in Southern California. However, it does rarely happen that it rains quite a bit in short bursts."

When something is solemn, it is a serious affair. A "solemn" church service is one that is weighty and given importance. A "solemn" speech is one that is given on an important day or about an important matter. To do something "solemnly" is to do it in a way that recognizes such importance. In contrast to this, to do something "frivolously" is to treat it as being unimportant. This is derived from the adjective "frivolous," meaning not having a serious value. It is also related to "frivolity," meaning light-hearted activity without any real weight.

A number of these wrong answers are trying to appeal to biases that have been created by stereotypes in our culture regarding being politically liberal. However, such stereotypes are unadvisable—both in day to day life and when answering a question like this one. Therefore, we must look for another answer. The adjective "liberal" means generous when used in a phrase like "a liberal amount of water." The adverb "barely" is a good contrast to "liberally"—think of "barely enough water" and "liberally poured water."