How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U? The words thus formed need not necessarily have any meaning.
- (a) 6
- (b) 8
- (c) 10
- (d) 12 ✓ UPSC's answer
Why the answer is (d)
• The word QUEUE consists of 5 letters: Q, U, E, U, E.
• The condition states that Q is always followed by U, so we treat the pair (QU) as a single unit or block.
• The remaining letters are E, U, and E.
• Thus, we are arranging 4 items: the block (QU), U, E, and E.
• The number of distinct permutations of these 4 items, where E is repeated twice, is calculated as 4! / 2!.
• 4! / 2! = (24) / 2 = 12, which matches option (d).
Why the other options are wrong
- (a) 6
- Option (a) is incorrect because 6 is the result of 3! / 1!, which ignores the extra U and one E or miscalculates the factorial division.
- (b) 8
- Option (b) is incorrect because 8 does not correspond to the standard permutation formula for this set of letters and constraints.
- (c) 10
- Option (c) is incorrect because 10 is not the result of the permutation calculation 4! / 2!.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.