  We study the ground state properties of a mixture formed by two spin-1
condensates in the absence of an external magnetic field. As the collisional
symmetry between interspecies bosonic atoms is broken, the interspecies
coupling interaction ($\beta $) and interspecies singlet pairing interaction
($\gamma $) arise. The ground state can be calculated using the angular
momentum theory analytically for $\gamma =0$. The full quantum approach of
exact diagonalization is adopted numerically to consider the more general case
as $\gamma \neq 0$. We illustrate the competition between the two interspecies
interactions and find that as singlet pairing interaction dominates (or the
total spin vanishes), there are still different types of singlet formations
which are well determined by $\beta $.
