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The correct order of energies of molecular orbitals of $N _2$ molecule, is
$\sigma 1 s < \sigma^* 1 s < \sigma 2 s < \sigma^* 2 s < \left(\pi 2 p_{ x }=\pi 2 p_{ y }\right) < \left(\pi^* 2 p_{ x }=\pi^* 2 p_{ y }\right) < \sigma 2 p_{ z } < \sigma^* 2 p_{ z }$
$\sigma 1 s < \sigma^* 1 s < \sigma 2 s < \sigma^* 2 s < \left(\pi 2 p_{ x }=\pi 2 p_{ y }\right) < \sigma 2 p_{ z } < \left(\pi^* 2 p_{ x }=\pi^* 2 p_{ y }\right) < \sigma^* 2 p_{ z }$
$\sigma 1 s < \sigma^* 1 s < \sigma 2 s < \sigma^* 2 s < \sigma 2 p_{ z } < \left(\pi 2 p_{ x }=\pi 2 p_{ y }\right) < \left(\pi^* 2 p_{ x }=\pi^* 2 p_{ y }\right) < \sigma^* 2 p_{ z }$
$\sigma 1 s < \sigma^* 1 s < \sigma 2 s < \sigma^* 2 s < \sigma 2 p_{ z } < \sigma^* 2 p_{ z } < \left(\pi 2 p_{ x }=\pi 2 p_{ y }\right) < \left(\pi^* 2 p_{ x }=\pi^* 2 p_{ y }\right)$
Solution
For molecules like $B _2, C _2, N _2$ etc. the increasing order of energies of various molecular orbitals is $\sigma 1 s < \sigma^* 1 s < \sigma 2 s < \sigma^* 2 s < \left(\pi 2 p_{ x }=\pi 2 p_{ y }\right) < \sigma 2 p_{ z } < \left(\pi^* 2 p_{ x }=\pi^* 2 p_{ y }\right) < \sigma^* 2 p_{ z }$
