The correct answer is: A. Equal angles back to back.
The radius of gyration is a measure of how far the mass of an object is concentrated from its center of mass. A larger radius of gyration indicates that the mass of the object is more concentrated near its center of mass, and a smaller radius of gyration indicates that the mass of the object is more spread out.
In a double angle section, the two angles are back to back, with their legs perpendicular to each other. The minimum radius of gyration is the radius of gyration about the axis that passes through the centers of the two angles.
For equal angles back to back, the minimum radius of gyration is given by:
$r_g = \frac{2}{3} \frac{d}{2}$
where $d$ is the distance between the centers of the two angles.
For unequal legged angles with long legs back to back, the minimum radius of gyration is given by:
$r_g = \frac{2}{3} \frac{d}{2} \sqrt{\frac{1}{2} + \frac{b^2}{a^2}}$
where $a$ is the length of the long leg and $b$ is the length of the short leg.
For unequal legged angles with short legs back to back, the minimum radius of gyration is given by:
$r_g = \frac{2}{3} \frac{d}{2} \sqrt{\frac{1}{2} + \frac{a^2}{b^2}}$
As you can see, the minimum radius of gyration is always larger for equal angles back to back than it is for unequal legged angles with either the long legs or the short legs back to back. This is because the mass of the object is more concentrated near the center of mass for equal angles back to back than it is for unequal legged angles.