The correct option is D Viscosity decreases with increase in temperature for a liquid and increases with increase in temperature for a gas.
Viscosity of a liquid (ηL) is due to the cohesion between its molecules. With increase in temperature of a liquid, cohesive forces decrease, because the separation between liquid molecules increases. This leads to the decrease in viscosity of a liquid.
In case of gases, the force of cohesion between molecules is very low, due to the high average speed of gas molecules. Viscosity of a gas (ηg) is due to the momentum transfer between its molecules. With the increase in the temperature of a gas, molecular motion increases, leading to the rise in viscosity of the gas.