Answer:
1. Because she studied (a positive), but couldn't (a negative word), it means that you must use "but" or another word to describe it:
Lara studied several hours every night, but she couldn't earn higher than a B on the daily quizzes.
2. This is a run-on sentence, because it is best to separate both of them. However, if added together, there is need of a comma:
After Audie Murphy had proved himself a true hero in World War II, he became a hero of the silver screen in many actions films.
3. Again, this is a run-on sentence in which it would be best to separate both of the sentence fragments. However, since this is not an answer choice, it is best to separate using a comma:
The invention of the telescope led later astronomers to the discovery of countless celestial objects, yet it failed at the time to bring its inventor the recognition he was due.
4. He awoke from his nap while riding in the passenger seat of the car, Brian was surprised to discover that his father had driven several hundred miles.
"When he awoke from his nap" is a better choice, because while it describes the past, it should be put from a present-time view, which means that it must connect to the present-time from the past.
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