Instead of hunting for one error in each sentence, we can build the grammatically correct version from scratch and then see which option matches it.
Start with the subject: "a few judges" is plural, so the verb must be "have," not "has." Next comes the possessive word before "vacation": since it belongs to the judges, it has to be the plural "their," not the singular "its," and it cannot be left out altogether. Finally, "cases" is plural, so the article in front of it has to be "the," not "a," because we are talking about specific, already known pending cases.
Putting these three pieces together gives: "A few judges have cut short their vacation to clear the long pending cases."
Now compare this built sentence with the options. Option A swaps "the" for "a" before "cases" and breaks the article rule. Option B drops "their" before "vacation" and leaves the sentence incomplete. Option C uses "has" instead of "have" and "its" instead of "their," breaking two rules at once. Only option D matches the sentence built from the rules exactly.
So, the correct answer is A few judges have cut short their vacation to clear the long pending cases.
A practical way to work through a sentence like this is to read each option aloud, exactly as it is written, and notice the very first spot where your ear catches something wrong before checking why.
Trusting the ear and then confirming with the grammar behind each stumble leads to the same result each time.
So, the correct answer is A few judges have cut short their vacation to clear the long pending cases.