Wire Combinations & Special Cases question from JEE Main 2022 (26 Jul, Shift 1)

In an experiment to determine the Young's modulus of wire of a length exactly $1\text{ m}$, the extension in the length of the wire is measured as $0.4\text{ mm}$ with an uncertainty of $\pm 0.02\text{ mm}$ when a load of $1\text{ kg}$ is applied. The diameter of the wire is measured as $0.4\text{ mm}$ with an uncertainty of $\pm 0.01\text{ mm}$. The error in the measurement of Young's modulus $(\Delta \text{Y})$ is found to be $x \times 10^{10}\text{ Nm}^{-2}$. The value of $x$ is _________________. $($take $\text{g} = 10\text{ ms}^{-2}$)