The irregularity in the amount of rainfall in different parts of the north Indian plains is mainly due to option 1, which is the irregular intensity of low pressure in the northwest parts of India.
To understand this, it is important to know that low pressure systems are responsible for the formation and movement of weather systems, including rainfall. In the Indian subcontinent, the northwest parts experience a significant influence from the monsoon winds, which bring in moist air from the Arabian Sea and the Bay of Bengal.
The intensity of low pressure systems in these areas can vary, leading to fluctuations in the amount of rainfall received. Sometimes, the intensity may be high, resulting in heavy rainfall, while at other times, it may be weak, leading to less rainfall or even dry spells.
The other options can be ruled out as they do not directly address the irregularity in rainfall. Option 2 mentions the variation in the location of the axis of low pressure trough, but it does not explain why this variation causes irregular rainfall. Option 3 mentions the difference in the frequency of cyclones, which are separate weather systems and may not be directly related to rainfall patterns. Option 4 mentions the variation in the amount of moisture carried by winds, which is a factor that influences rainfall but does not