The total energy radiated by a body per unit time per unit area $E \propto T^4$. Hence option $(c)$ is wrong.

Energy radiated per second is given by $\frac{Q}{t} = PA\varepsilon \sigma {T^4}$

==> $\frac{{{P_1}}}{{{P_2}}} = \frac{{{A_1}}}{{{A_2}}}.{\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^4} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}.{\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^4} = {\left( {\frac{1}{4}} \right)^2}\left( {\frac{{4000}}{{200}}} \right) = \frac{1}{1}$
 $\because P1 = P2$ , hence option $(d)$ is wrong.

Newton's law is an approximate form of Stefan's law of radiation and works well for natural convection. Hence option $(b)$ is correct.