The example above is not a sentence but a sentence fragment. Every proper sentence must have a subject and a main verb; this sentence contains neither (note that infinitives, while a verb form, do not function as a main verb). The correct choice is "They were unable to fix the device."

The example above is a sentence fragment. Every proper sentence must have a subject and a main verb. This sentence contains neither, but is simply a prepositional phrase. The correct choice is "He studied in the library"and conveys the point of the sentence, which is a simple sentence, so no other punctuation or changes are necessary.

The above example is a sentence fragment. Any proper sentence must have a subject and a main verb. Three options have subjects and verbs, but only one has the correct punctuation. The phrase "On New Year's Day" is an example of an introductory phrase, explaining information necessary to the context of the sentence, but outside of the main sentence, grammatically. These types of phrases must be followed by a comma in order to separate them from the rest of the sentence. The rest of the sentence is correct and needs no alteration. The correct choice is, "On New Year's Day, Jenna decided to start working towards accomplishing all of her dreams."

The example above is a sentence fragment. All proper sentences must contain a subject and a main verb. While a subject is present, there is no main verb present in the sentence. Four of the choices fix this, but "While making plans for the party, Tom invited all the guests" is the correct choice because it is in the active voice, and contains no excess punctuation. 

The above example is a sentence fragment. The verb "becoming" always needs an object of some sort (the word does not make any sense without one). The only example that provides an adequate direct object for the word (and therefore completing the sentence) is, "the traditional office environment seems to be becoming obsolete."

All of the incorrect answer choice present sentence fragment errors. The noun phrase "knowing your options" represents the subject of a clause. The subject requires a verb to complete the independent clause. The correct answer choice adjusts the beginning of the sentence with "The clause "you should know," resolving the sentence fragment error.

This sentence contains an error in subject-verb agreement. Since the subject of the sentence is "she" (3rd person, singular), the correct form of the word is "gives." The other choices are passive (e.g. given, was given), not proper forms (e.g. gived), or fragments (e.g. giving). The correct choice is, "She gives tips on how."

"As to whether" should always be just "whether." The same is true for "which." Finally, adding a comma to the section renders it incorrect.  

In this sentence, the participial phrase "initially meant to provide new forms of interest for the salesman" is an interrupting phrase, a phrase that provides extra meaning to the sentence, but is not a necessary part of the sentence's construction. All such phrases must be set apart from the rest of the sentence by commas. "The competition, initially meant to provide new forms of interest for the salesman, soon created" is the only answer choice which makes such a change.

Sentences should almost always be written in the active voice, rather than the passive voice. There is no need for parentheses, and "their" is correct, not "they're." So "They will always love their dog" is the best answer.