How can BN be paramagnetic?
This is the general MO diagram you need to fill with the valence electrons of BN



Boron has 3 valence electrons, and nitrogen has 5 valence electrons, this makes 8 electrons.

You have to start filling the orbitals from those with lowest energy to those with higher energy.

So, 2 electrons on $\sigma_\mathrm{2s}$, two electrons on $\sigma_\mathrm{2s}^*$, two electrons on $\sigma_\mathrm{2p}$. You have now 2 electrons left, and two orbitals of the same energy.

In this case, you need to follow Hund's rule, which states that  if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs. So you will have to put one electron on the $\pi_x$ orbital and another one on the $\pi_y$ orbital.
So you end up with 2 umpaired electrons, and paramagnetism of the molecule is explained.