The plots of intensity $(I)$ versus wavelength $(\lambda)$ for three black bodies at temperatures $T_1, T_2$ and $T_3$ respectively are as shown. Their temperatures are such that:

$A$ black body emits radiation of maximum intensity at wavelength $\lambda$ at temperature $T \ K$. Its corresponding wavelength at temperature $1.5 \ T \ K$ will be

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 $B$?

The maximum wavelength of radiation emitted by a star is $289.8 \ nm$. The intensity of radiation for the star is (Given: Stefan's constant $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$,Wien's constant $b = 2898 \ \mu m \ K$)

Solar radiation emitted by the sun resembles that emitted by a black body at a temperature of $6000 \ K$. Maximum intensity is emitted at a wavelength of about $4800 \ \mathring{A}$. If the sun were to cool down from $6000 \ K$ to $3000 \ K$,then the peak intensity would occur at a wavelength of ....... $\mathring{A}$.

Two stars $A$ and $B$ radiate maximum energy at the wavelengths of $360 \ nm$ and $480 \ nm$ respectively. Then the ratio of the surface temperatures of $A$ and $B$ is