The sentence in question reads: "There is no (E) answer to this question."
We are looking for a word that logically and grammatically fits in the context of expressing uncertainty or a lack of finality regarding a conclusion.
I. definitive (Correct):
"Definitive" means conclusive, final, or decisive and is commonly used in the phrase "no definitive answer." It accurately conveys that the answer is not absolute or final, making it the best fit.
II. vivid (Incorrect):
"Vivid" means clear, strong, or detailed in terms of imagery or description. It doesn't pair well with the word "answer" in this context. A "vivid answer" isn't a standard or meaningful collocation when referring to certainty.
III. absolution (Incorrect):
"Absolution" refers to forgiveness or release from guilt, typically in a religious context. It doesn't logically fit with the word "answer" here.
Thus, option (b) is the correct answer.