Explanation:

- Mean Proportional: The mean proportional (or geometric mean) between two numbers \(a\) and \(b\) is given by the square root of their product: \(\sqrt{a \times b}\). So, the mean proportional between 3.6 and 12.1 is \(\sqrt{3.6 \times 12.1} = 6.6\).

- Third Proportional: Given two numbers \(a\) and \(b\), the third proportional is a number \(c\) such that \(a : b = b : c\). Solving \(c\), we have \(c = \frac{b^2}{a}\). So, the third proportional to 2 and 11 is \(\frac{11^2}{2} = 60.5\).

- Ratio: We need the ratio of the mean proportional and third proportional, which is \(6.6 : 60.5\). Simplifying gives approximately \(6 : 55\).

- Answer Options:

- Option 1: 11 : 36

- Option 2: 36 : 5

- Option 3: 6 : 5

- Option 4: 6 : 55