Explanation

The use of the word “though” establishes a contrast between the blank, which requires a description of the judge’s standing, and “phony allegations of wrongdoing.” Thus the words that best complete the blank must indicate that the judge’s reputation was not adversely affected by these allegations. The only words that do so are “undiminished” and “undamaged” (Choices B and D), which produce sentences alike in meaning. “Undecided” and “unresolved” also produce sentences alike in meaning, but neither word makes sense when inserted into the blank.
Thus the correct answer is undiminished (Choice B) and undamaged (Choice D).
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Answers : B,D

"though shaken by allegation" is the clue; we need to look for contrast words - undiminished and undamaged fit into it.

Ans (B, D)

The judge’s standing in the legal community, though shaken by phony allegations of wrongdoing, emerged, at long last, _________ .

There is a time contrast between the judge's standing then and now. At long last, what was the status of his standing? His previous standing was shaken by phony allegations of wrong doing. The contrast word "though" indicates that the situation now is the exact opposite. Hence his standing would have emerged unaffected or unsullied. The words from the choice list is undiminished and undamaged.
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