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Q. According to MOT,$ C_2$ molecule has

MP PMTMP PMT 2007Chemical Bonding and Molecular Structure

Solution:

$C_2(12)=\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \pi 2p^2_x \approx\pi 2p^2_y$
$C_2$ has two pairs of electrons in $\pi2p_x\, and\, \pi2p_y$ therefore, it has only two $\pi$-bonds.