If letters of the word 'KUBER' are written in all possible orders and arranged as in a dictionary, then rank of the word 'KUBER' will be

Options

A. 67
B. 68
C. 69
D. 65

Answer

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

### Step 1: List the letters in alphabetical order
The letters in 'KUBER' are: K, U, B, E, R.
Arranging them in alphabetical order gives us: B, E, K, R, U.

### Step 2: Count the words starting with letters before 'K'
1. **Words starting with 'B':**
- Remaining letters: E, K, R, U
- The number of arrangements = 4! = 24

2. **Words starting with 'E':**
- Remaining letters: B, K, R, U
- The number of arrangements = 4! = 24

Now, we have counted all the words starting with letters before 'K':
- Total words = 24 (from B) + 24 (from E) = 48

### Step 3: Count the words starting with 'K'
Now we consider words starting with 'K':
- The next letter in 'KUBER' is 'U'.

#### Step 3.1: Count words starting with 'KA', 'KB', 'KE'
1. **Words starting with 'KB':**
- Remaining letters: E, R, U
- The number of arrangements = 3! = 6

2. **Words starting with 'KE':**
- Remaining letters: B, R, U
- The number of arrangements = 3! = 6

3. **Words starting with 'KR':**
- Remaining letters: B, E, U
- The number of arrangements = 3! = 6

Now, we have counted all the words starting with 'K' and letters before 'U':
- Total words = 6 (from KB) + 6 (from KE) + 6 (from KR) = 18

### Step 4: Count the words starting with 'KU'
Now we consider words starting with 'KU':
- The next letter in 'KUBER' is 'B'.

#### Step 4.1: Count words starting with 'KUB'
1. **Words starting with 'KUB':**
- Remaining letters: E, R
- The number of arrangements = 2! = 2

2. **Words starting with 'KUE':**
- Remaining letters: B, R
- The number of arrangements = 2! = 2

Now, we have counted all the words starting with 'KU' and letters before 'B':
- Total words = 2 (from KUB) + 2 (from KUE) = 4

### Step 5: Count the word 'KUBER'
Finally, we have reached the word 'KUBER'. We add 1 for the word itself.

### Step 6: Calculate the total rank
Total rank = 48 (from B and E) + 18 (from K with letters before U) + 4 (from KU with letters before B) + 1 (for KUBER itself) = 48 + 18 + 4 + 1 = 71.

Thus, the rank of the word 'KUBER' is **71**.