To answer this question about the types of drought in India, let's analyze each statement in detail:

1. Meteorological Drought:
   • This type of drought occurs when there is a significant decrease in the amount of precipitation over an area over a certain period, usually a season or a year. In the context of India, it is often defined by rainfall deficiency. The statement is slightly misworded in the original form. However, if we consider the Indian Meteorological Department (IMD) norms, a meteorological drought is declared when annual rainfall is less than 75% of the normal levels.
   • The statement "A meteorological drought occurs when the mean annual rainfall is less than 75%" is essentially correct when we interpret it as below normal levels, aligning it with IMD norms.
2. Agricultural Drought:
   • This type of drought refers to inadequate soil moisture to support agriculture, which happens when drought conditions lead to a lack of soil moisture necessary for crop growth.
   • The statement "Agricultural drought arises out of extreme moisture stress" is correct, as moisture stress affects crop yield directly.
3. Soil Moisture Drought:
   • This form of drought is specifically related to the lack of moisture in the soil, which can affect agriculture and natural vegetation.
   • It is closely linked to meteorological drought, as prolonged periods of low precipitation lead to reduced soil moisture.
   • The statement "Soil moisture drought is related to meteorological drought" is correct because meteorological drought often precipitates soil moisture drought.

Thus, all three statements are correct according to the standard definitions and understanding of droughts in an Indian context. Therefore, the correct answer is: