UPSC NDA 2 2022 Mathematics Solved Paper

Concept:Use combinations to select letters and permutations to arrange them.Explanation:The word "QUESTION" consists of 8 distinct letters.There are 4 vowels: U, E, I, O and 4 consonants: Q, S, T, N.Number of ways to choose 2 vowels from 4: $^{4}C_{2} = 6$.Number of ways to choose 2 consonants from 4: $^{4}C_{2} = 6$.Total ways to select the two vowels and two consonants: $6 \times 6 = 36$.Now, arrange these 4 distinct letters: $4! = 24$ ways.Therefore, total number of 4-letter words: $36 \times 24 = 864$.Hence, the correct option is D (864).Answer:864