Kirchhoff's Law of Radiation and Theoretical Proof

A black pattern on a porcelain bowl appears brighter than the rest of bowl, when it is strongly heated and taken to a dark room. This is an illustration of

Two perfect black bodies $A_1$ and $A_2$ made out of same material have diameters $2 \mathrm{cm}$ and $16 \mathrm{cm}$ respectively. $\lambda {\text{'}}_{\max }$ and $\lambda \text{'}{\text{'}}_{\max }$ are the wavelengths corresponding to their maximum radiation of energy at a common temperature $\lambda {\text{'}}_{\max }$ and $\lambda \text{'}{\text{'}}_{\max }$ are related as 

Three objects coloured black, grey and white can withstand hostile conditions up to $2800 °\mathrm{C}$. These objects are thrown into a furnace where each of them attains a temperature of $2000 °\mathrm{C}$. Which object will glow brightest? 

A hot and a cold body are kept in a vacuum separated from each other. Which of the following causes a decrease in the temperature of the hot body?

Sweet makers do not clean the bottom of cauldron because

At temperature $T$, the emissive power and absorption power of a body for certain wavelength are $e_{\lambda }$ and $a_{\lambda }$, respectively, then

If $E$ Represents emissivity of a substance ,$E_b$ Represents emissivity of black body and $a$ Represents coefficient of absorption, then correct equation out of the following is

Ratio of emissive power and absorptive power of all substances is equal to the emissive power of black body under the same condition. This law is