The correct answer is option 1, meaning that both the assertion (A) and reason (R) are true, and R is the correct explanation of A.

In the assertion, it states that anti-cyclonic conditions, referring to high pressure weather systems, are formed in the winter season when the atmospheric pressure is high and temperatures are low. This is accurate because during winter, the cooler air contributes to the increase in atmospheric pressure, leading to the creation of an anti-cyclone.

The reason explains that the winter rainfall in Northern India causes the development of these anti-cyclonic conditions along with low temperatures. This is also true, as precipitation often leads to changes in air pressure - in this case, it increases and contributes to the formation of anti-cyclones.

The reason correctly explains the assertion, as it provides clarity on one of the factors contributing to the formation of anti-cyclonic conditions during the winter season. Therefore, option 1 is the right answer.