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 $S_2$?

Three black discs $x, y, z$ have radii $1 \ m, 2 \ m$ and $3 \ m$ respectively. The wavelengths corresponding to maximum intensity are $200 \ nm, 300 \ nm$ and $400 \ nm$ respectively. The relation between emissive power $E_x, E_y$ and $E_z$ is:

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:

If the wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5 \times 10^{-6} \ m$ and $10^{-4} \ m$ respectively,the ratio of their temperatures is:

$A$ black body is at a temperature of $2880\;K$. The energy of radiation emitted by this object with wavelength between $499\;nm$ and $500\;nm$ is ${U_1}$,between $999\;nm$ and $1000\;nm$ is ${U_2}$ and between $1499\;nm$ and $1500\;nm$ is ${U_3}$. The Wien's constant $b = 2.88 \times {10^6}\;nm\,K$. Then

Two spherical bodies $A$ (radius $6 \,cm$) and $B$ (radius $18 \,cm$) are at temperatures $T_1$ and $T_2$,respectively. The maximum intensity in the emission spectrum of $A$ is at $500 \,nm$ and in that of $B$ is at $1500 \,nm$. Considering them to be black bodies,what will be the ratio of the rate of total energy radiated by $A$ to that of $B$?