Option 1 states that landslides are sudden and sporadic. This statement is incorrect. Landslides are not always sudden in nature and can occur gradually over time. They are not sporadic, as they can be triggered by various factors such as heavy rainfall, earthquakes, or human activities.

Option 2 states that landslides result when the slope is gentle. This statement is incorrect. Landslides can occur on slopes of various steepness, not just gentle ones. Factors such as the geology of the area, the type of soil, and the presence of vegetation can all contribute to the occurrence of landslides.

Option 3 states that mining activity is also responsible for landslides. This statement is correct. Mining activity can destabilize slopes, leading to landslides. The removal of vegetation, alteration of the natural drainage patterns, and excavation of slopes can all increase the risk of landslides in mining areas.

Based on the above analysis, the correct option is option 2, which states that only statement 1 and 3 are correct.