The correct option is C B<Be<C
Ionisation energy increses as we move from left to right in a period because effective nuclear charge increases and thus more energy will be required to remove an electron.
Accordingly one can expect the order of 1st ionisation energy as Be<B<C.
Be has higher first ionisation energy because of its fully- filled s orbital whereas B has only one electron in 2p- orbital. We know s-orbital has higher penetration power than p -orbital and in Be electron is removed from s- orbital and in B electron will be removed from p-orbital.
Therefore, correct increasing order of 1st ionisation energy is B<Be<C