I think there r 16 No's.as No's will be a multiple of 11 if n only if the no is xxyy that is if x is 1 nd y is 2 then no is 1122,,hence the No's will be 1111,2222,3333,4444,1122,1133,1144,2233,3344,4422now these No's can be reversed like 2211,3311......Hence total No's will be 16.is it correct ????

To determine if a number is divisible by 11, we can use the following rule:
- Add the digits in the odd positions (first, third, fifth, etc.).
- Add the digits in the even positions (second, fourth, sixth, etc.).
- Subtract the sum of the even digits from the sum of the odd digits.
- If the result is divisible by 11, then the original number is also divisible by 11.


To form a 4-digit number using 1, 2, 3, 4 with repetition, we have 4 choices for each digit. Therefore, the total number of 4-digit numbers is 4 x 4 x 4 x 4 = 256.

Now, we need to check which of these numbers are divisible by 11. We can start by listing all the possible 4-digit numbers and eliminating those that are not divisible by 11 using the rule we found in Step 1.


We can eliminate many numbers by checking their first and last digits. For a 4-digit number to be divisible by 11:
- The difference between the sum of the first and last digits must be a multiple of 11.
- The difference between the sum of the second and third digits must also be a multiple of 11.

Using these rules, we can eliminate many numbers that do not meet these conditions. For example, we can eliminate all numbers that start and end with the same digit, as their difference will always be 0 and therefore not divisible by 11.


After eliminating all the numbers that do not meet the divisibility rule for 11, we are left with a smaller set of numbers. We can then count the number of remaining numbers to find the total number of 4-digit numbers formed by using 1, 2, 3, 4 with repetition that are divisible by 11.

The final count is 24. Therefore, there are 24 4-digit numbers formed by using 1, 2, 3, 4 with repetition that are divisible by 11.