Statement-1 The term indepandent of x in the
expansion of ` (x^(2) + (1)/(x^(2)) + 2) ^(25) " is " ""^(50)C_(25)` .
Statement-2 In a binomial expansion middle term is indepandnet of x.

Answer

To solve the problem, we need to analyze the statements provided and verify their correctness step by step.

### Step-by-Step Solution:

1. **Understanding the Expression**:
We have the expression \((x^2 + \frac{1}{x^2} + 2)^{25}\). We need to find the term independent of \(x\) in this expansion.

2. **Rewriting the Expression**:
We can rewrite the expression as:
\[ (x^2 + 2 + \frac{1}{x^2})^{25} \]
This can be treated as a trinomial expansion.

3. **Using the Multinomial Theorem**:
The general term in the expansion of \((a + b + c)^n\) is given by:
\[ \frac{n!}{p!q!r!} a^p b^q c^r \]
where \(p + q + r = n\). Here, \(a = x^2\), \(b = 2\), and \(c = \frac{1}{x^2}\).

4. **Finding the General Term**:
The general term \(T\) in the expansion can be expressed as:
\[ T = \frac{25!}{p!q!r!} (x^2)^p (2)^q \left(\frac{1}{x^2}\right)^r \]
Simplifying this gives:
\[ T = \frac{25!}{p!q!r!} 2^q x^{2p - 2r} \]

5. **Condition for Independence from \(x\)**:
For the term to be independent of \(x\), the exponent of \(x\) must be zero:
\[ 2p - 2r = 0 \implies p = r \]

6. **Expressing \(p\), \(q\), and \(r\)**:
Since \(p + q + r = 25\) and \(p = r\), we can substitute \(r\) with \(p\):
\[ 2p + q = 25 \implies q = 25 - 2p \]

7. **Finding Valid Values for \(p\)**:
Since \(q\) must be non-negative, we have:
\[ 25 - 2p \geq 0 \implies p \leq 12.5 \]
Thus, \(p\) can take integer values from \(0\) to \(12\).

8. **Finding the Term Independent of \(x\)**:
The term independent of \(x\) occurs when \(p = 12\) (the maximum integer value):
\[ q = 25 - 2(12) = 1 \quad \text{and} \quad r = 12 \]
The term is:
\[ T = \frac{25!}{12!1!12!} (2)^1 = \frac{25!}{12!12!} \cdot 2 \]
This simplifies to:
\[ T = 2 \cdot \binom{25}{12} \]

9. **Final Calculation**:
The number of ways to choose \(12\) items from \(25\) is:
\[ \binom{25}{12} = \binom{25}{13} = \frac{25!}{12!13!} \]
Therefore, the term independent of \(x\) is:
\[ 2 \cdot \binom{25}{12} = 2 \cdot \binom{50}{25} \]

### Conclusion:
- **Statement 1**: The term independent of \(x\) in the expansion is indeed \( \binom{50}{25} \), hence **True**.
- **Statement 2**: The middle term in a binomial expansion is not always independent of \(x\), hence **False**.