The temperature of earth is maintained by a dynamic equilibrium between sun and Earth. Sun & Earth can be assumed to be black bodies:

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If the power output of sun would double by changing the temperature, equilibrium temperature of earth also doubles

If the radius of sun doubles without changing it's power, its surface temperature would decrease by factor of 2

If the radius of earth doubles without any change in sun. It’s equilibrium temperature would increase by factor of 2

If the distance between earth and sun would increases by a factor of 2, the equilibrium temperature of earth would decreases by factor of 2

answer is B.

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Detailed Solution

Power output of Sun=δ14πRs2Ts4⇒TS∝1RST1T2=R2R1⇒T1T2=2RR⇒T2=T12Power received by Earth=δ14πRs2Ts44πd2πRE2=δ14πRE2TE4⇒TE∝1dT1T2=d2d1⇒T1T2=2dd⇒T2=T12

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