Consider the following reactions:
i. `CO(g)+H_(2)O(g) hArr CO_(2)(g)+H_(2)(g), K_(1)`
ii. `CH_(4)(g)+H_(2)O(g) hArr CO(g)+3H_(2)(g), K_(2)`
iii. `CH_(4)(g)+2H_(2)O(g) hArr CO_(2)(g)+4H_(2)(g), K_(3)`
Which of the following is/are incorrect?

Options

A. `K_(3)=K_(1)//K_(2)`
B. `K_(3)=K_(1)^(2)//K_(2)^(3)`
C. `K_(3)=K_(1)xxK_(2)`
D. `K_(3)=K_(1)sqrt(K_(2))`

Explanation

To solve the problem, we need to analyze the given chemical reactions and their corresponding equilibrium constants. Let's break it down step by step.

### Step 1: Write down the reactions and their equilibrium constants
1. **Reaction 1**:
\[ \text{CO}(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g), \quad K_1 \]

2. **Reaction 2**:
\[ \text{CH}_4(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}(g) + 3\text{H}_2(g), \quad K_2 \]

3. **Reaction 3**:
\[ \text{CH}_4(g) + 2\text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + 4\text{H}_2(g), \quad K_3 \]

### Step 2: Combine the first two reactions
To find a relationship between the equilibrium constants, we can add Reaction 1 and Reaction 2.

- **Adding Reaction 1 and Reaction 2**:
\[ \text{CO}(g) + \text{H}_2\text{O}(g) + \text{CH}_4(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g) + \text{CO}(g) + 3\text{H}_2(g) \]

- Simplifying this, we cancel out CO on both sides:
\[ \text{CH}_4(g) + 2\text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + 4\text{H}_2(g) \]

### Step 3: Relate the equilibrium constants
According to the principle of equilibrium constants:
- When two reactions are added, their equilibrium constants multiply.
Thus, we have:
\[ K_3 = K_1 \times K_2 \]

### Step 4: Identify incorrect statements
Now we need to determine which statements regarding the equilibrium constants are incorrect. Based on our derivation:
- The correct relationship is \( K_3 = K_1 \times K_2 \).
- Any statement claiming otherwise (like \( K_1 \) or \( K_2 \) being equal to \( K_3 \) or any other incorrect relationships) would be incorrect.

### Conclusion
The incorrect statements among the options provided would be those that do not align with \( K_3 = K_1 \times K_2 \).