For a perfectly black body,a graph is plotted between the frequency of radiation with maximum intensity $(v_m)$ and the absolute temperature $T$. Which of the following graphs is correct?

If the wavelengths of maximum intensity of radiation emitted by the Sun and the Moon are $0.5 \times 10^{-6} \, m$ and $10^{-4} \, m$ respectively,then the ratio of their temperatures is ............

The wavelength of maximum emission from a body at a temperature of $200 \, K$ is $14 \, \mu m$. If the temperature of the body is increased to $1000 \, K$,find the new wavelength of maximum emission.

Which of the following is the $\nu_m - T$ graph for a perfectly black body? ($\nu_m$ = maximum frequency of radiation,$T$ = absolute temperature)

On observing light from three different stars $P, Q$ and $R$, it was found that the intensity of violet colour is maximum in the spectrum of $P$, the intensity of green colour is maximum in the spectrum of $R$, and the intensity of red colour is maximum in the spectrum of $Q$. If $T_P, T_Q$ and $T_R$ are the respective absolute temperatures of $P, Q$ and $R$, then it can be concluded from the above observations that:

Star $S_1$ emits maximum radiation of wavelength $420 \, nm$ and the star $S_2$ emits maximum radiation of wavelength $560 \, nm$. What is the ratio of the temperature of $S_1$ and $S_2$?