$A$ black body has a maximum wavelength $\lambda_m$ at $2000\,K$. Its corresponding wavelength at $3000\,K$ will be:

On investigation of light from three different stars $A, B$ and $C$, it was found that in the spectrum of $A$ the intensity of red colour is maximum, in $B$ the intensity of blue colour is maximum and in $C$ the intensity of yellow colour is maximum. From these observations, it can be concluded that

The radiation energy density per unit wavelength at a temperature $T$ has a maximum at a wavelength $\lambda_0$. At temperature $2T$,it will have a maximum at a wavelength:

If 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

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 $b = 2898 \ \mu m \ K$)

The Sun emits light with a maximum wavelength of $510 \, nm$,while another star $X$ emits light with a maximum wavelength of $350 \, nm$. What is the ratio of the surface temperature of the Sun to that of star $X$?