Correct statements of the following based on molecular orbital theory

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LUMO orbitals is in N₂ molecule have one horizontal plane along inter nuclear axis and are one vertical plane

O₂ molecule is paramagnetic if inter mixing of 2s-2p Orbitals takes place

$C_{2}$ molecule has four electrons in HOMO which is responsible for two $π$ bonds

when 2s-2p orbital mixing is not possible in C₂ it is paramagnetic containing one sigma one pi bond and paramagnetic

answer is A, B, C, D.

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Detailed Solution

If inter mixing is possible
$K K < σ 2 S^{2} < σ^{*} 2 S^{2} < π_{x} = π_{y} < σ_{P Z} < {π^{*}}_{x} = {π^{*}}_{z} < {σ^{*}}_{2 p z}$
If inter mixing not possible
$K K < σ 2 S^{2} < σ^{*} 2 S^{2} < σ_{p z} < π_{x} = π_{y} < {π^{*}}_{x} = {π^{*}}_{z} < {σ^{*}}_{2 p z}$
HOMO = highest occupied molecular orbitals
LUMO = Lowest unoccupied molecular orbitals