Three of the following number-pairs are alike in some manner and hence form a group. Which number-pair does not belong to that group? (Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)

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Let's analyze each pair:

1. 14 – 121
   121 is 11 squared (11^2 = 121).
   14 - 11 = 3

2. 21 – 361
   361 is 19 squared (19^2 = 361).
   21 - 19 = 2

3. 18 – 256
   256 is 16 squared (16^2 = 256).
   18 - 16 = 2

4. 11 – 81
   81 is 9 squared (9^2 = 81).
   11 - 9 = 2

Now, check the difference between the first number and the square root of the second number:
- Pair 1 difference: 3
- Pair 2 difference: 2
- Pair 3 difference: 2
- Pair 4 difference: 2

Three pairs (2, 3, and 4) have a difference of 2 between the first number and the square root of the second number.
Pair 1 has a difference of 3, so it does not belong to the group.

However, the question asks which number-pair does not belong to the group. The pair with difference 3 is 14 – 121.

Re-examining the options, the pair 14 – 121 is the odd one out.

Therefore, the correct answer is 14 – 121.

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