To determine the magnetic nature of the given complexes, we analyze the oxidation state, electronic configuration, and the nature of the ligands for each central metal atom/ion:
[MnBr4]2−: Mn2+ has a 3d5 configuration. Br− is a weak field ligand. The complex is tetrahedral with 5 unpaired electrons. (Paramagnetic)
[NiCl4]2−: Ni2+ has a 3d8 configuration. Cl− is a weak field ligand. The complex is tetrahedral with 2 unpaired electrons. (Paramagnetic)
[Ni(CN)4]2−: Ni2+ has a 3d8 configuration. CN− is a strong field ligand. The complex is square planar (dsp2) with all electrons paired. (Diamagnetic)
[Ni(CO)4]: Ni0 has a 3d84s2 configuration, which becomes 3d10 in the presence of the strong field ligand CO. The complex is tetrahedral with all electrons paired. (Diamagnetic)
[CoF6]3−: Co3+ has a 3d6 configuration. F− is a weak field ligand. The complex is octahedral and high spin (t2g4eg2) with 4 unpaired electrons. (Paramagnetic)
[Fe(CN)6]4−: Fe2+ has a 3d6 configuration. CN− is a strong field ligand. The complex is octahedral and low spin (t2g6eg0) with all electrons paired. (Diamagnetic)
[Mn(CN)6]3−: Mn3+ has a 3d4 configuration. CN− is a strong field ligand. The complex is octahedral and low spin (t2g4eg0) with 2 unpaired electrons. (Paramagnetic)
[Ti(CN)6]3−: Ti3+ has a 3d1 configuration. The complex is octahedral (t2g1eg0) with 1 unpaired electron. (Paramagnetic)
[Cu(H2O)6]2+: Cu2+ has a 3d9 configuration. The complex is octahedral (t2g6eg3) with 1 unpaired electron. (Paramagnetic)
[Co(C2O4)3]3−: Co3+ has a 3d6 configuration. Oxalate (C2O42−) acts as a strong field ligand for Co3+. The complex is octahedral and low spin (t2g6eg0) with all electrons paired. (Diamagnetic)
Therefore, the paramagnetic complexes are [MnBr4]2−, [NiCl4]2−, [CoF6]3−, [Mn(CN)6]3−, [Ti(CN)6]3−, and [Cu(H2O)6]2+.
The total number of paramagnetic complexes is 6.
Answer: 6