The correct answer is - a) decrease.
The barometer is an instrument that measures the air pressure, thus the barometric pressure term. The warm, moist air will result in the decrease in the barometric pressure. The reason for that is that the warm and moist air is lighter because the molecules are further apart, so the air pressure drops.
If the air is cold and dry, than the air pressure will increase, and the reason for that is that the molecules are much closer, so the air is heavier. The rainfall also manages to increase the weight of the air, thus increasing the air pressure.
