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:

Two stars $P$ and $Q$ are observed at night. Star $P$ appears reddish while star $Q$ is white. From this we conclude:

The maximum wavelength of radiations emitted at $900\,K$ is $4\,\mu m$. What will be the maximum wavelength of radiations emitted at $1200\,K$ (in $,\mu m$)?

$A$ black body at a temperature of $3000 \ K$ cools down. The wavelength corresponding to maximum energy density shifts by $\Delta \lambda = 9 \ \mu m$. What is the new temperature of the black body (in $K$)? (Given $b = 3 \times 10^{-3} \ m \cdot K$)

Which one of the following is the $\nu_{m}-T$ graph for a perfectly black body? Here, $\nu_{m}$ is the frequency of radiation with maximum intensity and $T$ is the absolute temperature.

Two bodies $A$ and $B$ have emissivities $0.01$ and $0.81$ respectively. The outer surface areas of both bodies are the same. Both bodies emit total radiant power at the same rate. The wavelength $\lambda_B$ corresponding to the maximum spectral radiance of $B$ is $1.0 \mu m$. If the temperature of $A$ is $5802 \ K$,calculate the wavelength $\lambda_A$ in $\mu m$. (Note: The original question asked for $\lambda_B$ but provided $\lambda_B$ as $1.0 \mu m$ and asked for $\lambda_A$ based on the context of the solution provided).