For a reaction of reversible nature , net rate is `((dx)/(dt))=k_(1)[A]^(2)[B]^(1)-k_(2)[C]`, hence , given reactionis:

Options

A. `2A +(1)/(B) C`
B. `2A-B C`
C. `2A C-B`
D. None of these

Explanation

To solve the problem, we need to analyze the given net rate expression for a reversible reaction and identify the correct reaction that corresponds to it. The net rate is given as:

\[ \frac{dx}{dt} = k_1 [A]^2 [B] - k_2 [C] \]

### Step 1: Understand the net rate expression
The net rate expression indicates that the rate of the forward reaction is dependent on the concentrations of reactants \(A\) and \(B\), while the rate of the backward reaction is dependent on the concentration of product \(C\).

### Step 2: Identify the forward and backward reactions
The forward reaction can be represented as:
\[ 2A + B \rightarrow C \]
This means that for the forward reaction, the rate can be expressed as:
\[ \text{Rate}_{\text{forward}} = k_1 [A]^2 [B] \]

The backward reaction can be represented as:
\[ C \rightarrow 2A + B \]
The rate for the backward reaction can be expressed as:
\[ \text{Rate}_{\text{backward}} = k_2 [C] \]

### Step 3: Write the net rate expression
Combining the rates of the forward and backward reactions gives us the net rate:
\[ \frac{dx}{dt} = \text{Rate}_{\text{forward}} - \text{Rate}_{\text{backward}} = k_1 [A]^2 [B] - k_2 [C] \]

### Step 4: Verify with the given options
Now we need to check if the above expression matches with any of the given reactions.

1. **Option A: \(2A + \frac{1}{B} \rightarrow C\)**
- This does not match the form of the net rate expression because the stoichiometry does not align with the given rate expression.

2. **Option B: \(2A + B \rightarrow C\)**
- This matches the net rate expression derived above. The forward reaction rate is \(k_1 [A]^2 [B]\) and the backward reaction rate is \(k_2 [C]\).

3. **Option C: \(2A \rightarrow C + B\)**
- This does not match either, as the stoichiometry does not align with the given rate expression.

### Conclusion
The reaction that corresponds to the net rate expression given in the question is:
\[ 2A + B \rightarrow C \]

### Final Answer
The correct answer for the given question is **Option B**: \(2A + B \rightarrow C\).

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