  We present new features of low energy Bogoliubov quasiparticle excitations of
a two component Bose-Einstein condensate (TBEC) in quasi-2D geometry at zero
temperature using Hartree-Fock-Bogoliubov (HFB). We, in particular, consider
the TBECs of $^{133}$Cs~-$^{87}$Rb and $^{85}$Rb~-$^{87}$Rb, and show specific
features in the low energy excitation spectrum as a function of the interaction
strength. For $^{85}$Rb~-$^{87}$Rb TBEC, the appearance of a new zero energy
mode is observed. Whereas for $^{133}$Cs~-$^{87}$Rb TBEC we report a
bifurcation of the softened Kohn mode at the point of transition from miscible
to immiscible domain. The lower energy mode, after the bifurcation, goes soft
and becomes a new Goldstone mode of the system.
