Resistivity: $\rho=\dfrac{m}{ne^2\tau}$

In a metal, the number density $n$ of free (conduction) electrons is essentially fixed (already all valence electrons are free) and does not change appreciably with temperature. However, as temperature rises, lattice vibrations increase, causing more frequent electron-ion collisions, so the relaxation time $\tau$ DECREASES.

Since $\rho\propto1/\tau$, this decrease in $\tau$ (with $n$ nearly unchanged) causes $\rho$ to increase with temperature.

Answer: (C) $\tau$ decreases with temperature but $n$ does not change appreciably