In the following question, four multiples of 11 are given. Three of them are not perfect squares, and one is a perfect square. Select the odd number from the given alternatives.

Introduction / Context:
This numerical reasoning question involves identifying a special property among multiples of 11. Odd one out problems like this check understanding of factors, squares, and basic number relationships. Recognising perfect squares is especially important in many competitive exams, since squares often appear in algebra, geometry, and data interpretation questions.

Given Data / Assumptions:
- The options given are 121, 44, 66, 111, and 132.
- Each of these numbers is a multiple of 11, so they all share a basic factor based property.
- A perfect square is an integer that can be written as n * n for some integer n.
- Exactly one of these multiples of 11 is also a perfect square, which makes it the odd one out.

Concept / Approach:
The main concept here is to identify which number is a perfect square. Every option is a multiple of 11, so simply checking divisibility by 11 will not help us separate them. Instead, we need to see which number can be written as the square of an integer. We can quickly test the nearby square numbers and see whether any match the given options. The number that is a perfect square while the others are not will be the answer.

Step-by-Step Solution:
Step 1: List some square numbers close to our options. For example, 10^2 = 100, 11^2 = 121, and 12^2 = 144.Step 2: Notice that 121 appears exactly as 11^2. Therefore 121 is a perfect square and a multiple of 11.Step 3: Examine 44. It is equal to 4 * 11. There is no integer n such that n * n = 44, so it is not a perfect square.Step 4: Examine 66. It is 6 * 11 and again does not equal any integer square.Step 5: Examine 111. It is 11 * 10 plus 1, but it is not equal to n * n for any integer n, so it is not a perfect square.Step 6: Examine 132. It is 12 * 11 and again not equal to any integer square.Step 7: Since only 121 is both a multiple of 11 and a perfect square, it is different from the others and is the odd one out.

Verification / Alternative Check:
We can also verify by considering the square roots. The square root of 121 is exactly 11, an integer. The approximate square root of 44 is a little above 6, but not an integer. The square root of 66 is between 8 and 9, but not an integer. The square root of 111 is a little more than 10, and again not an integer. The square root of 132 is between 11 and 12, but not an integer. Since only 121 gives an integer square root, it confirms that 121 is the only perfect square in the list and is therefore the odd one out.

Why Other Options Are Wrong:
44 is not correct as the odd one out because, although it is a multiple of 11, it lacks the special square property and is just like 66, 111, and 132 in this respect. 66 is also a non square multiple of 11 and so does not stand out in this group. 111 is again a multiple of 11 but not a perfect square, so it remains in the main category. 132 is similar, as it is only a regular multiple of 11. Only 121 has the distinct property of being 11 * 11, which the question is designed to highlight.

Common Pitfalls:
Sometimes students focus only on the number of digits and might be tempted to choose 44 or 66 because they are two digit numbers, or 111 because it looks special with repeated digits. However, the test setter expects you to recognise the perfect square pattern. To avoid mistakes, always recall common squares like 11^2 = 121 and 12^2 = 144 and compare them with the options provided. This small habit can significantly improve accuracy in questions about square numbers and odd one out patterns.

Final Answer:
121