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We study the energy eigenvalue and the yrast states for a harmonically two-component weak-interacting BoseEinstein condensate (BEC) when the intra-species and interspecies scattering length are different. The energy shift for different energy eigenvalues related to intra- and interspecies scattering lengths is calculated with the per-turbation method. The actual yrast spectrum is more complicated than that when intra-species and interspecies scattering length are equal. The degenerated features disappear and so do the perfect symmetric features.