<p>If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is</p>
Step-by-Step Solution
Key Concept: Count all permutations that come alphabetically before QUEEN by fixing earlier letters and counting remaining arrangements. QUEEN has letters E, E, N, Q, U where E repeats twice, so use the formula for permutations with repetition.
<p><strong>Step 1:</strong> List letters of QUEEN in alphabetical order: E, E, N, Q, U</p><p><strong>Step 2:</strong> Count words starting with letters before Q (alphabetically):</p><p>• Words starting with E: Remaining letters are E, N, Q, U → arrangements = 4! = 24</p><p>• Words starting with N: Remaining letters are E, E, Q, U → arrangements = 4!/2! = 12</p><p><strong>Step 3:</strong> Now fix Q as first letter. Count words of form Q___ where blanks are filled with E, E, N, U in alphabetical order:</p><p>• Words starting with QE: Remaining letters are E, N, U → arrangements = 3! = 6</p><p>• Words starting with QN: Remaining letters are E, E, U → arrangements = 3!/2! = 3</p><p><strong>Step 4:</strong> Now fix QU as first two letters. Remaining letters: E, E, N</p><p>• Words starting with QUE: Remaining letters are E, N → arrangements = 2! = 2</p><p>These are QUEEN and QUENE</p><p><strong>Step 5:</strong> QUEEN comes first among these two arrangements</p><p><strong>Total position:</strong> 24 + 12 + 6 + 3 + 1 = <strong>46</strong></p><p>∴ Answer: D</p>
Correct Answer: D