All the words that can be formed using alphabets A, H, L, U and R are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is

Options

A. 71
B. 72
C. 73
D. 74

Answer

To find the rank of the word "RAHUL" when all permutations of the letters A, H, L, U, and R are arranged in alphabetical order, we can follow these steps:

### Step-by-Step Solution:

1. **List the Letters in Alphabetical Order**:
The letters A, H, L, R, U in alphabetical order are:
- A, H, L, R, U

2. **Count Words Starting with Each Letter Before 'R'**:
- **Words starting with 'A'**:
If 'A' is the first letter, the remaining letters are H, L, R, U. The number of permutations of these 4 letters is:
\[ 4! = 24 \]
- **Words starting with 'H'**:
If 'H' is the first letter, the remaining letters are A, L, R, U. The number of permutations of these 4 letters is:
\[ 4! = 24 \]
- **Words starting with 'L'**:
If 'L' is the first letter, the remaining letters are A, H, R, U. The number of permutations of these 4 letters is:
\[ 4! = 24 \]

3. **Count Words Starting with 'R'**:
Now we consider words that start with 'R'. The next letter in "RAHUL" is 'A'.
- **Words starting with 'RA'**:
The remaining letters are H, L, U. The number of permutations of these 3 letters is:
\[ 3! = 6 \]
- **Words starting with 'RH'**:
The remaining letters are A, L, U. The number of permutations of these 3 letters is:
\[ 3! = 6 \]
- **Words starting with 'RL'**:
The remaining letters are A, H, U. The number of permutations of these 3 letters is:
\[ 3! = 6 \]

4. **Count Words Starting with 'RAH'**:
Now we consider words that start with 'RAH'. The next letter in "RAHUL" is 'U'.
- **Words starting with 'RAH'**:
The remaining letters are L. The only permutation is:
\[ 1! = 1 \]
- **Words starting with 'RAHU'**:
The remaining letter is L. The only permutation is:
\[ 1! = 1 \]

5. **Calculate the Total Rank**:
Now we can sum up all the permutations calculated:
- From 'A': 24
- From 'H': 24
- From 'L': 24
- From 'RA': 6
- From 'RH': 6
- From 'RL': 6
- From 'RAH': 1
- From 'RAHU': 1

Total:
\[ 24 + 24 + 24 + 6 + 6 + 6 + 1 + 1 = 92 \]

6. **Rank of 'RAHUL'**:
Since we need the rank of "RAHUL", we add 1 (for the word "RAHUL" itself):
\[ 92 + 1 = 93 \]

Thus, the rank of the word "RAHUL" is **93**.