The potential difference across a conductor of resistivity $\rho$ is constant. The heat generated in the conductor is directly proportional to

The formula for heat generated $H$ under constant potential difference $V$ over time $t$ is:
$$H=\frac{V^2}{R}t$$
The resistance $R$ of a conductor is given by:
$$R=\rho \frac{l}{A}$$
Substitute $R$ into the heat equation:
$$H=\frac{V^2}{\rho \frac{l}{A}}t=\left(\frac{V^{2}At}{l}\right)\frac{1}{\rho }$$
Since $V$, $A$, $l$, and $t$ are constants, the heat generated is directly proportional to the inverse of resistivity:
$$H\propto \frac{1}{\rho }$$
(Note: The exam text printed $\rho$ as 'e')