UPSC NDA 2 2022 Mathematics Solved Paper

Concept:Treat all consonants as a single block and then arrange this block along with the vowels.Explanation:Consider the word "QUESTION", which has 8 distinct letters.It contains 4 vowels (U, E, I, O) and 4 consonants (Q, S, T, N).To keep all consonants together, consider them as one group.The 4 consonants can be arranged within this group in $4! = 24$ ways.Now we have 5 items to arrange: the 4 vowels and the 1 consonant group.These 5 items can be arranged in $5! = 120$ ways.Total number of words formed = $24 \times 120 = 2880$.Answer:2880 (Option B).