First ionisation potential of C- atom is greater than that of B atom , where as the revers is true is for second ionisation potential.

Explanation

Electron configuration of carbon
`(Z=6)1s^(2)2s^(2)2p^(2)`.
Electron configuration of boron
`(Z=5)1s^(2)2s^(2)2p^(1)`.
The size of a carbon atom is smaller than boron . So the valence electron of carbon has greater nuclear charge than of boron . Hence the first I.E of carbon is greater than that of boron.
However , the second ionization enthalpy of boron is higher than that of carbon . This is because after losing 1 electron , Boron has a fully filled orbital `(2s^(2))` than carbon `(2p^(1))` . Fully filled orbitals so greater amount of energy will be needed to remove an electron from boron .So in this case , the second I.E of boron is higher than that of carbon.