The construction of this sentence makes it clear that the two parts of this compound sentence are contrasted with one another. This makes the use of the conjunction "and" to join the two a mistake, as the conjunction "but" is used to draw a sharp contrast between the two parts. As the only answer choice to use the correct conjunction, "his school days, but his post-graduation depression" is the correct answer choice.

In this case, no conjunction is needed between the two clauses. This is because the part of the sentence before the comma consists of a subordinate clause, not an independent clause. In other words, this part of the sentence cannot stand on its own. Commas followed by conjunctions are used to combine two independent clauses into a compound sentence, and since this sentence consists of a subordinate clause and an independent clause instead of two independent clauses, a comma is sufficient and the conjunction ("and") is not only unnecessary, but grammatically incorrect.

The example sentence begins with a negative word ("Neither") and uses the corresponding negative conjunction ("nor"); therefore, it must either be changed to begin with the subject, or changed to add a "do" verb immediately after "neither." In modern English it is considered smoother, and more common, to simply begin the sentence with the subject, and then treat the negative conjunction normally, rather than adding a "do" verb, but adding a "do" verb would also be grammatically correct. Of the options provided, the best solution to this conjunction error would be, "She neither faltered nor hesitated when questioned under oath."

This is a case in which we need to decide whether to use the word "which" or "that" to introduce the clause set apart from the rest of the sentence by commas. "That" is used to introduce information absolutely necessary to the sentence's meaning, whereas "which" is used to introduce information that would not change the sentence's meaning if it were removed from the sentence. Information that is not crucial to the sentence's meaning is usually set apart by commas.

In this case, the sentence "The last time it snowed, my dad lost control of his car and hit a tree" still makes sense, so we know that the information included between the commas isn't absolutely necessary to the sentence's meaning. Plus, the information in question is being set apart from the rest of the sentence by commas. So, we should use "which," and not "that."

The example sentence makes use of an incorrect conjunction. "Such" is used to indicate a result, whereas "so" is used (as a conjunction) to indicate purpose. Because the sentence is discussing someone's precautionary measure, the correct conjunction here is "so". "She carefully reviewed her case notes, so as not to be surprised in court."

The original sentence is constructed in such a way that its two clauses are meant to contrast each other. In this instance, there is no need for any conjunction after the comma since the second clause stands in clear contrast to the first without one. 

The original sentence consists of two clauses, the second of which is the result of the first. "But" is therefore not an appropriate conjunction to use in this sentence, and the inclusion of the word "so" is enough to demonstrate cause and effect.

The second clause in the sentence is intended to stand in contrast to the first, so the best conjunction to use in this instance is "but."

Because the second independent clause contradicts the first in this compound sentence it is more correct to separate the two with the conjunction "but," not "and."

When connecting two independent clauses using a coordinating conjunction, one should use a comma after the word preceding the conjunction. When the sentences seem to contrast, it is most likely most appropriate to implement "but" rather than "and". The incorrect answers all show errors of this kind. Some of the incorrect answer choices also incorrectly use the relative pronoun "that" in place of the preposition "of," resulting in a syntactic error.