The relation between the colour and the temperature of a star is given by

$A$ black body has a maximum wavelength $\lambda_{m}$ at a temperature of $2000 \ K$. Its maximum wavelength at $3000 \ K$ will be:

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?

The wavelength of the radiation emitted by a black body is $6 \ mm$ and Wien's constant is $3 \times 10^{-3} \ mK$. Then the temperature of the black body is (in $K$)

$A$ black body radiates power $P$ and maximum energy is radiated by it at a wavelength $\lambda_0$. The temperature of the black body is now changed such that it radiates maximum energy at the wavelength $\frac{\lambda_0}{4}$. The power radiated by it at the new temperature is (in $P$)

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 $X$?