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Close-coupling calculations based on an R-matrix formalism are performed for the 1s-2p resonance photoionizations from the low-lying states of boron-like carbon ions. The resonance energies, widths and oscillator strengths of 1s-2p core excitations are determined by analysing the calculated photoionization cross sections. Our calculations are in reasonable agreement with the experimental and theoretical results presented by other authors. The present numerical values may help to analyse the astrophysical and laboratory plasmas.