UPSC Prelims 2026 · CSAT
Question 9: Basic Numeracy
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.
AnswerUPSC’s answer is (d).
Q must be followed by U, so glue them into one block QU. You then arrange four items: the block, the spare U and two identical Es. That gives 4!/2! = 12 words. Each word has a single Q, so its partner U is fixed and no word is counted twice.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows UPSC’s provisional key; the final key could change it.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong: 6 undercounts; it ignores the freedom to place the block among the other three letters.
- (b) Wrong: 4! = 24 divided by 2 for the two Es is 12, not 8.
- (c) Wrong: 10 does not match 4!/2!.
- (d) Right: four items with two identical Es give 24/2 = 12.
Only the provisional key (27 May 2026) was found; the final key replaces it when found.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.