The letters of the word "KANPUR" are arranged in all possible ways as in a dictionary, the rank of the word 'KANPUR' from last is

Options

A. 121
B. 122
C. 598
D. 599

Answer

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

### Step-by-Step Solution:

1. **Identify the letters and their arrangement**:
The letters in "KANPUR" are K, A, N, P, U, R. First, we need to arrange these letters in alphabetical order:
- A, K, N, P, R, U

2. **Calculate the total number of arrangements**:
Since all letters are unique, the total number of arrangements of the letters in "KANPUR" is given by \(6!\) (factorial of 6):
\[ 6! = 720 \]

3. **Find the rank of "KANPUR"**:
To find the rank of "KANPUR", we need to count how many words would come before it in alphabetical order.

4. **Count words starting with letters before 'K'**:
- Words starting with 'A': The remaining letters are K, N, P, U, R. The number of arrangements is \(5!\):
\[ 5! = 120 \]
So, there are 120 words starting with 'A'.

5. **Count words starting with 'K'**:
Now we consider words starting with 'K'. The next letter in "KANPUR" is 'A'.

6. **Count words starting with 'KA'**:
- Remaining letters are N, P, R, U. The number of arrangements is \(4!\):
\[ 4! = 24 \]
So, there are 24 words starting with 'KA'.

7. **Count words starting with 'KAN'**:
Now we consider words starting with 'KAN'. The next letter in "KANPUR" is 'P'.

8. **Count words starting with 'KANP'**:
- Remaining letters are R, U. The number of arrangements is \(2!\):
\[ 2! = 2 \]
So, there are 2 words starting with 'KANP'.

9. **Count words starting with 'KANPU'**:
The next letter in "KANPUR" is 'U'.

10. **Count words starting with 'KANPUR'**:
- The only arrangement left is 'R', which means "KANPUR" is the next word.

11. **Calculate the rank**:
Now we can calculate the rank of "KANPUR":
\[ \text{Rank of KANPUR} = 120 + 24 + 2 + 1 = 147 \]

12. **Calculate the rank from the last**:
To find the rank from the last, we subtract the rank from the total arrangements:
\[ \text{Rank from last} = 720 - 147 + 1 = 574 \]

### Final Answer:
The rank of the word "KANPUR" from the last is **574**.