`2A rarrB +C`
It would be a zero order reaction when

Options

A. The rate of reaction is proportional to sequare of conc of A
B. The rate of reaction remains same at any conc of A
C. The rate remains unchanged at any conc of B and C
D. The rate of reaction doubles if conc of B is increased to double

Answer

To determine when the reaction \( 2A \rightarrow B + C \) is a zero-order reaction, we need to analyze the rate of the reaction in relation to the concentration of the reactants.

### Step 1: Understand the Rate Expression
For any reaction, the rate can be expressed as:
\[ \text{Rate} = k [A]^n \]
where \( k \) is the rate constant, \( [A] \) is the concentration of the reactant, and \( n \) is the order of the reaction.

### Step 2: Define Zero-Order Reaction
In a zero-order reaction, the order \( n \) is equal to 0. Therefore, the rate expression simplifies to:
\[ \text{Rate} = k [A]^0 = k \]
This means that the rate of the reaction is constant and does not depend on the concentration of the reactant \( A \).

### Step 3: Analyze the Options
Now, let's evaluate the given statements:

1. **Option 1**: The rate of reaction is proportional to the square of the concentration of \( A \).
- This is incorrect because, for a zero-order reaction, the rate does not depend on the concentration of \( A \).

2. **Option 2**: The rate of reaction remains the same at any concentration of \( A \).
- This is correct. Since the rate is constant (equal to \( k \)), it does not change with varying concentrations of \( A \).

3. **Option 3**: The rate remains unchanged at any concentration of \( B \) and \( C \).
- This is incorrect. The rate of a zero-order reaction is independent of the concentrations of products \( B \) and \( C \) as well.

4. **Option 4**: The rate of reaction doubles if the concentration of \( B \) is increased to double.
- This is also incorrect. The rate remains constant regardless of the concentration of products.

### Conclusion
The only statement that correctly describes a zero-order reaction is:
- **Option 2**: The rate of reaction remains the same at any concentration of \( A \).

### Final Answer
The reaction \( 2A \rightarrow B + C \) is a zero-order reaction when the rate of reaction remains the same at any concentration of \( A \).

---