The correct option is that Statement-I is incorrect, but Statement-II is correct. Statement-I is inaccurate because while incoming solar radiation does warm the Earth's surface, it is the longwave radiation emitted by the Earth's surface that primarily heats the atmosphere through processes such as convection and radiation, making terrestrial radiation a significant contributor to atmospheric warming. Statement-II is correct because greenhouse gases such as carbon dioxide absorb and re-radiate longwave infrared radiation effectively, which is fundamental to the greenhouse effect that helps to maintain the Earth's average temperature. This understanding is essential in climate science and aligns with concepts found in standard UPSC-level sources, such as NCERT textbooks on geography and environmental science.