Explanation

(a) Resistance of a wire $R = \frac{\rho L}{A} = \frac{4\rho L}{\pi D^{2}}$ where $D$ is diameter of wire
As $R \propto L\ and\ R \propto \frac{1}{D^{2}}$, hence it is clear that resistance will be maximum if $\frac{L}{D^{2}}$ is maximum. On calculation we find
$\frac{L}{D^{2}}$ maximum when, $L = 50$ cm and $D = 0.5$ mm