How is the temperature of stars determined?

If $\lambda_{m}$ denotes the wavelength at which the radioactive emission from a black body at a temperature $T \; K$ is maximum,then

$A$ black disc has a radius $R$ and the wavelength corresponding to the maximum intensity is $\lambda$. The emissive power $(E)$ for the different radii and maximum wavelengths is directly proportional to:

An extremely hot star would appear to be

The black body spectrum of an object $O_1$ is such that its radiant intensity (i.e.,intensity per unit wavelength interval) is maximum at a wavelength of $200\,nm$. Another object $O_2$ has the maximum radiant intensity at $600\,nm$. The ratio of power emitted per unit area by source $O_1$ to that of source $O_2$ is

The law used in the measurement of the temperature of stars is .........