Which graph represents the $v_m - T$ relationship for a black body,where $v_m$ is the frequency corresponding to the maximum energy emission and $T$ is the absolute temperature?

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \, nm$. The radiation intensity of the star is (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 is at a temperature of $2880\;K$. The energy of radiation emitted by this object with wavelength between $499\;nm$ and $500\;nm$ is ${U_1}$,between $999\;nm$ and $1000\;nm$ is ${U_2}$ and between $1499\;nm$ and $1500\;nm$ is ${U_3}$. The Wien's constant $b = 2.88 \times {10^6}\;nm\,K$. Then

$A$ 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 new temperature,the emissive power is:

Two stars $A$ and $B$ radiate maximum energy at wavelengths $3.9 \times 10^{-7} \text{ m}$ and $5.2 \times 10^{-7} \text{ m}$ respectively. The ratio of the temperature of star $A$ to that of star $B$ will be

Ordinary bodies $A$ and $B$ radiate maximum energy at wavelengths differing by $4 \mu m$. The absolute temperature of body $A$ is $3$ times that of body $B$. The wavelength at which body $B$ radiates maximum energy is: (in $\mu m$)