UPSC NDA I 2016 General Ability Solved Paper

Concept:The apparent brightness of a star depends on both its intrinsic properties (size and temperature) and its distance from the observer.Explanation:The power radiated by a star (its luminosity) is given by the Stefan‑Boltzmann law:$P = \sigma A T^4$, where $A$ is the surface area and $T$ is the temperature.For a spherical star, $A = 4\pi r^2$, so $P = 4\pi r^2 \sigma T^4$.A larger radius $r$ (size) and higher temperature $T$ increase the radiated power, making the star intrinsically brighter.However, the brightness we observe (apparent brightness) also depends on the distance from Earth.For a given luminosity, a star appears dimmer if it is farther away.Thus, the apparent brightness depends on size, temperature, and distance from the Earth.Answer:size, temperature, and distance from the earth (Option D).