Let $x_0 = [a], x_1 = [2a] - [a], x_2 = [3a] - [2a], x_3 = [3a] - [4a],x_4 = [5a] - [4a],x_5 = [6a] - [5a], . . . , $ where $a=\frac{\sqrt{2013}}{\sqrt{2014}}$ .The value of $x_9$ is: 

(A): $2$ (B): $3$ (C): $4$ (D): $5$ (E): None of the above.
1. First, we need to understand the notation $[x]$, which represents the floor function, i.e., the greatest integer less than or equal to $x$.
2. Given $a = \frac{\sqrt{2013}}{\sqrt{2014}} = \sqrt{\frac{2013}{2014}}$.
3. We need to find the value of $x_9 = [10a] - [9a]$.

Let's calculate $10a$ and $9a$ step by step:

4. Calculate $10a$:
   \[
   10a = 10 \cdot \sqrt{\frac{2013}{2014}} = \sqrt{100 \cdot \frac{2013}{2014}} = \sqrt{\frac{201300}{2014}}
   \]
   Since $\frac{201300}{2014} \approx 99.5$, we have:
   \[
   \sqrt{\frac{201300}{2014}} \approx \sqrt{99.5} \approx 9.975
   \]
   Therefore, $[10a] = [9.975] = 9$.

5. Calculate $9a$:
   \[
   9a = 9 \cdot \sqrt{\frac{2013}{2014}} = \sqrt{81 \cdot \frac{2013}{2014}} = \sqrt{\frac{162117}{2014}}
   \]
   Since $\frac{162117}{2014} \approx 80.5$, we have:
   \[
   \sqrt{\frac{162117}{2014}} \approx \sqrt{80.5} \approx 8.975
   \]
   Therefore, $[9a] = [8.975] = 8$.

6. Now, we can find $x_9$:
   \[
   x_9 = [10a] - [9a] = 9 - 8 = 1
   \]

The final answer is $\boxed{1}$.