The correct answer is A. Increases.
The resistance of a conductor is proportional to its length and inversely proportional to its cross-sectional area. In a carbon filament lamp, the filament is a long, thin wire that is heated by the current flowing through it. As the voltage increases, the current increases, which causes the filament to heat up more. The increased heat causes the filament to expand, which decreases its cross-sectional area. This decrease in cross-sectional area causes the resistance of the filament to increase.
Option B is incorrect because the resistance of a conductor increases as its temperature increases. Option C is incorrect because the resistance of a conductor is not constant. Option D is incorrect because the resistance of a carbon filament lamp does increase as the applied voltage increases.