An experiment measured quantity a, b, c and then x is calculated from `x = ab^(2)//c^(3)`. If the percentage error in a, b, c are `pm` 1%, `pm` 3% and `pm` 2% respectively, the percentage error in x can be,

Options

A. A) `pm` 13%
B. B) `pm` 7%
C. C) `pm` 4%
D. D) `pm` 1%

Explanation

To find the percentage error in the quantity \( x \) calculated from the formula \( x = \frac{a b^2}{c^3} \), we will use the rules of error propagation. The percentage error in a product or quotient can be calculated by summing the relative errors of the individual quantities involved, taking into account their respective powers.

### Step-by-step solution:

1. **Identify the formula**:
\[ x = \frac{a b^2}{c^3} \]

2. **Determine the percentage errors**:
- Percentage error in \( a \) is \( \pm 1\% \)
- Percentage error in \( b \) is \( \pm 3\% \)
- Percentage error in \( c \) is \( \pm 2\% \)

3. **Apply the error propagation formula**:
The percentage error in \( x \) can be calculated using the formula:
\[ \text{Percentage error in } x = \left( \text{Percentage error in } a \right) + 2 \times \left( \text{Percentage error in } b \right) + 3 \times \left( \text{Percentage error in } c \right) \]

4. **Substitute the values**:
- For \( a \): \( 1\% \)
- For \( b \): \( 3\% \), but since \( b \) is squared, we multiply by 2.
- For \( c \): \( 2\% \), but since \( c \) is cubed, we multiply by 3.

Therefore, we have:
\[ \text{Percentage error in } x = 1\% + 2 \times 3\% + 3 \times 2\% \]

5. **Calculate**:
\[ \text{Percentage error in } x = 1\% + 6\% + 6\% = 1\% + 12\% = 13\% \]

6. **Conclusion**:
The percentage error in \( x \) is \( \pm 13\% \).

### Final Answer:
The percentage error in \( x \) can be \( \pm 13\% \).