Write the relation for resistance of a wire

For a wire, $R = \rho \frac{L}{A}$ where $L$ is length and $A$ is cross-sectional area.

Express area in terms of diameter

For a circular wire, $A = \frac{\pi d^2}{4}$ Hence, $R = \rho \frac{4L}{\pi d^2}$

So, $R \propto \frac{L}{d^2}$

Use percentage error formula

For a quantity of the form $R \propto L^1 d^{-2}$ the maximum percentage error is $\frac{\Delta R}{R}\times 100 = \frac{\Delta L}{L}\times 100 + 2\frac{\Delta d}{d}\times 100$

Substitute the given errors

Given: $\frac{\Delta L}{L}\times 100 = 0.1\%$ $\frac{\Delta d}{d}\times 100 = 0.1\%$

Therefore, $\frac{\Delta R}{R}\times 100 = 0.1 + 2(0.1) = 0.3\%$

Match with the options

$0.3\%$ corresponds to Option D.

Comparison with stored answer

Stored correct answer: D

Derived answer: D

So they agree.