Which of the following is the $\nu_m - T$ graph for a perfectly black body? ($\nu_m$ = maximum frequency of radiation,$T$ = absolute temperature)

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

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:

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

$A$ black body radiates maximum energy at wavelength $\lambda$ and its emissive power is $E$. Now,due to a change in the temperature of that body,it radiates maximum energy at wavelength $\frac{2 \lambda}{3}$. At that temperature,the emissive power is: