Super-imposed?

The hour and minute hands are superimposed only when their angle is the same.
${\displaystyle {\begin{aligned}\theta _{\text{min}}&=\theta _{\text{hr}}\\\Rightarrow 6^{\circ }\times M&=0.5^{\circ }\times (60\times H+M)\\\Rightarrow 12\times M&=60\times H+M\\\Rightarrow 11\times M&=60\times H\\\Rightarrow M&={\frac {60}{11}}\times H\\\Rightarrow M&=5.{\overline {45}}\times H\end{aligned}}}$
H is an integer in the range $0-11.$ This gives times of: $0:00, 1:05.\overline{45}, 2:10.\overline{90}, 3:16.\overline{36}, 4:21.\overline{81}, 5:27.\overline{27}. 6:32.\overline{72}, 7:38.\overline{18}, 8:43.\overline{63}, 9:49.\overline{09}, 10:54.\overline{54},$ and $12:00.$ $(0.\overline{45}$ minutes are exactly $27.\overline{27}$ seconds.)

This is an easy problem, we have to think what does superimpose mean, it means they are at same angle from a point. Other options are eliminated easily as for any option there is some angle between hour and minute hands given by $|30h-5.5m|$