The letters of the word 'DELHI' are arranged in all possible ways as in a dictionary, the rank of the word 'DELHI' is

Options

A. 3
B. 5
C. 6
D. 7

Answer

To find the rank of the word "DELHI" when all the letters are arranged in alphabetical order, we can follow these steps:

### Step-by-Step Solution:

1. **Arrange the letters in alphabetical order:**
The letters of the word "DELHI" are D, E, H, I, L. Arranging them in alphabetical order gives us:
- D, E, H, I, L

2. **Identify the first letter of "DELHI":**
The first letter is D. Since D is the first letter in our alphabetical arrangement, we move to the next letter.

3. **Identify the second letter:**
The second letter is E. Since E is also the second letter in our alphabetical arrangement, we again move to the next letter.

4. **Identify the third letter:**
The third letter is L. The next letter in our alphabetical arrangement is H. Since L comes after H, we need to count how many words can be formed starting with "DE" and having letters that come before L.

5. **Count arrangements starting with "DEH":**
If we start with "DEH", the remaining letters are I and L. The number of arrangements of I and L is:
\[ 2! = 2 \]
(The arrangements are "DEHIL" and "DEHLI").

6. **Count arrangements starting with "DEI":**
If we start with "DEI", the remaining letters are H and L. The number of arrangements of H and L is:
\[ 2! = 2 \]
(The arrangements are "DEIHL" and "DEILH").

7. **Count arrangements starting with "DEL":**
Now we have "DEL" as the prefix. The next letter in "DELHI" is H, which matches the alphabetical order. We move to the next letter.

8. **Identify the fourth letter:**
The fourth letter is I. The next letter in alphabetical order is I, which matches again. We move to the last letter.

9. **Identify the fifth letter:**
The fifth letter is L. Since we have reached the end of the word "DELHI", we count this arrangement as well.

10. **Calculate the total rank:**
Now we sum all the counts:
- From "DEH": 2 arrangements
- From "DEI": 2 arrangements
- The arrangement "DELHI" itself counts as 1.

Thus, the total rank of "DELHI" is:
\[ 2 + 2 + 1 = 5 \]

### Final Answer:
The rank of the word "DELHI" is **5**.