<p>If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in a dictionary, then the word SACHIN appears at series number</p>
Step-by-Step Solution
Key Concept: Count the number of permutations that come before SACHIN in lexicographic (dictionary) order by fixing prefixes and counting arrangements of remaining letters.
<p>Letters of SACHIN in alphabetical order: A, C, H, I, N, S.</p><p>Words starting with A: $5! = 120$</p><p>Words starting with C: $5! = 120$</p><p>Words starting with H: $5! = 120$</p><p>Words starting with IA: $4! = 24$</p><p>Words starting with IC: $4! = 24$</p><p>Words starting with IH: $4! = 24$</p><p>Words starting with IN: $4! = 24$</p><p>Words starting with IS: $4! = 24$</p><p>Words starting with SA: $4! = 24$</p><p>Words starting with SC: $4! = 24$</p><p>Words starting with SH: $4! = 24$</p><p>Words starting with SI: $4! = 24$</p><p>Words starting with SN: $4! = 24$</p><p>Position = $120 + 120 + 120 + 5 \times 24 + 5 \times 24 + 1 = 600$.</p><p>∴ Answer is (d) 600.</p>
Correct Answer: D