We are asked to find the values of the given expressions involving absolute values and radicals, and then choose the corresponding labels from the given options.

1. Problem Description

We are asked to find the values of the given expressions involving absolute values and radicals, and then choose the corresponding labels from the given options.

2. Solution Steps

(1) $|-\sqrt{11}|$

The absolute value of a negative number is its positive counterpart.

$|-\sqrt{11}| = \sqrt{11}$.

The corresponding label is エ.

(2) $|3-9|$

First, evaluate the expression inside the absolute value:

$3-9 = -6$.

Then, take the absolute value:

$|-6| = 6$.

The corresponding label is イ.

(3) $|3-\sqrt{11}|$

Since $\sqrt{9} = 3$ and $\sqrt{16} = 4$, we know that $3 < \sqrt{11} < 4$. Thus, $3-\sqrt{11}$ is a negative number.

Therefore, $|3-\sqrt{11}| = -(3-\sqrt{11}) = -3 + \sqrt{11} = \sqrt{11} - 3$.

The corresponding label is キ.

(4) $|2\sqrt{11}-3|$

Since $\sqrt{9} = 3$ and $\sqrt{16} = 4$, $\sqrt{11}$ is slightly larger than $3$. Thus, $2\sqrt{11}$ is slightly larger than $6$. Therefore, $2\sqrt{11} - 3$ is a positive number.

Therefore, $|2\sqrt{11}-3| = 2\sqrt{11} - 3$.

The corresponding label is ク.

3. Final Answer

5: エ

6: イ

7: キ

8: ク