Question:
If all the letters of the word RANKS are permutated in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word RANKS is
If all the letters of the word RANKS are permutated in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word RANKS is
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Rank = (number of words before it) + 1.
Updated On: Jun 3, 2026
- $74$
- $76$
- $75$
- $77$
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The Correct Option is C
Solution and Explanation
Step 1: Concept
Count the number of words that appear before the given word in dictionary order.
Step 2: Meaning
Alphabetical order is \[ A<K<N<R<S. \]
Step 3: Analysis
First letter $R$: Letters before $R$ are $A,K,N$. \[ 3\times 4!=72. \] Now fix $R$. Second letter $A$: No remaining letter comes before $A$. Contribution $=0$. Third letter $N$: Among remaining letters $\{K,N,S\}$, only $K$ comes before $N$. \[ 1\times 2!=2. \] Fourth letter $K$: No smaller remaining letter. Contribution $=0$. Total words before RANKS: \[ 72+2=74. \] Hence rank \[ 74+1=75. \]
Step 4: Conclusion
Therefore the rank of RANKS is $75$.
Final Answer: (C)
Count the number of words that appear before the given word in dictionary order.
Step 2: Meaning
Alphabetical order is \[ A<K<N<R<S. \]
Step 3: Analysis
First letter $R$: Letters before $R$ are $A,K,N$. \[ 3\times 4!=72. \] Now fix $R$. Second letter $A$: No remaining letter comes before $A$. Contribution $=0$. Third letter $N$: Among remaining letters $\{K,N,S\}$, only $K$ comes before $N$. \[ 1\times 2!=2. \] Fourth letter $K$: No smaller remaining letter. Contribution $=0$. Total words before RANKS: \[ 72+2=74. \] Hence rank \[ 74+1=75. \]
Step 4: Conclusion
Therefore the rank of RANKS is $75$.
Final Answer: (C)
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