How is the temperature of stars determined?

Two identical balls $A$ and $B$ are heated. Ball $A$ appears blue and ball $B$ appears red. What is the relationship between their temperatures?

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

If a black wire of platinum is heated, its colour first appears red, then yellow, and finally white. This can be understood on the basis of:

$Assertion :$ For higher temperature, the peak emission wavelength of a blackbody shifts to lower wavelengths.
$Reason :$ Peak emission wavelength of a blackbody is proportional to the fourth power of temperature.

$A$ hot source emits maximum radiation energy at a wavelength of $11 \times 10^{-5} \ cm$. According to Wien's displacement law,for what value of $n$ will a source at a temperature $n$ times the original temperature emit maximum energy at a wavelength of $5.5 \times 10^{-5} \ cm$?