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 arranged in alphabetical order, we can follow these steps:

### Step 1: Arrange the letters in alphabetical order
The letters of the word 'DELHI' are D, E, L, H, and I. Arranging these letters in alphabetical order gives us:
- D, E, H, I, L

### Step 2: Count the words starting with letters before 'D'
Since 'D' is the first letter of 'DELHI', we do not need to count any words starting with letters before 'D'.

### Step 3: Count the words starting with 'D' and the next letter
Now we consider words that start with 'D'. The next letter in 'DELHI' is 'E'.

#### Step 3.1: Count words starting with 'DE'
Next, we look at words starting with 'DE'. The remaining letters are L, H, and I. The letters in alphabetical order are H, I, and L.

- The words that can be formed starting with 'DE' and then 'H':
- The remaining letters are L and I.
- The number of arrangements of L and I is 2! = 2.

#### Step 3.2: Count words starting with 'DEI'
Next, we look at words starting with 'DEI'. The remaining letters are L and H. The letters in alphabetical order are H and L.

- The words that can be formed starting with 'DEI' and then 'H':
- The remaining letter is L.
- The number of arrangements is 1! = 1.

### Step 4: Count the words starting with 'DEL'
Now we consider words starting with 'DEL'. The next letter in 'DELHI' is 'H'.

#### Step 4.1: Count words starting with 'DELH'
The remaining letter is 'I'. The only arrangement is 'I' itself.

### Step 5: Count the rank
Now we sum up all the counts:
- Words starting with 'D' and before 'E': 0
- Words starting with 'DE' and before 'L': 2 (from 'DEH' and 'DEI')
- Words starting with 'DEL' and before 'H': 1 (from 'DELI')

Now, we add 1 for the word 'DELHI' itself:
- Total rank = 0 + 2 + 1 + 1 = 4.

### Final Rank
Thus, the rank of the word 'DELHI' is 5.