Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule ${\mathrm{B}}_2$ is:

${\mathrm{B}}_2:{\left({\sigma }_{2_s}\right)}^2{\left({\sigma }_{2_s}^{\ast }\right)}^2\left(\pi 2p_x^2=\pi 2p_y^0\right)$

diamagnetic

${\mathrm{B}}_1{\mathrm{O}}_1=\frac{2}{2}=1$

So, the correct answer is 1 and diamagnetic.
Hence, the correct answer is A.