`[Fe(CN)_6]^(4-)`
`Fe(CN)_6]^(3-)`
`[Ti(CN)_6]^(3-)`
`[Ni(CN)_4]^(2-)`
`[Co(CN)_6]^(3-)`
Among the given complexes, number of paramagnetic complexes is ________________ .

Explanation

To determine the number of paramagnetic complexes among the given complexes, we need to analyze each complex based on the oxidation state of the metal and the electronic configuration. Paramagnetic complexes contain unpaired electrons, while diamagnetic complexes do not.

### Step-by-Step Solution:

1. **Identify the oxidation state of the metal in each complex:**
- For `[Fe(CN)_6]^{4-}`:
- CN is a neutral ligand, so the oxidation state of Fe is +2.
- For `[Fe(CN)_6]^{3-}`:
- The oxidation state of Fe is +3.
- For `[Ti(CN)_6]^{3-}`:
- The oxidation state of Ti is +3.
- For `[Ni(CN)_4]^{2-}`:
- The oxidation state of Ni is +2.
- For `[Co(CN)_6]^{3-}`:
- The oxidation state of Co is +3.

2. **Determine the electronic configuration of the metal ions:**
- **Fe (2+)**: 3d⁶
- **Fe (3+)**: 3d⁵
- **Ti (3+)**: 3d¹
- **Ni (2+)**: 3d⁸
- **Co (3+)**: 3d⁶

3. **Analyze the crystal field splitting:**
- CN is a strong field ligand, which causes pairing of electrons in the lower energy d-orbitals (t₂g).
- For each complex, we will fill the d-orbitals according to the strong field splitting.

4. **Fill the d-orbitals for each complex:**
- **[Fe(CN)₆]^{4-} (Fe²⁺, 3d⁶)**:
- Configuration: t₂g⁶ e₁g⁰ (all electrons are paired) → **Diamagnetic**
- **[Fe(CN)₆]^{3-} (Fe³⁺, 3d⁵)**:
- Configuration: t₂g⁵ e₁g⁰ (5 unpaired electrons) → **Paramagnetic**
- **[Ti(CN)₆]^{3-} (Ti³⁺, 3d¹)**:
- Configuration: t₂g¹ e₀ (1 unpaired electron) → **Paramagnetic**
- **[Ni(CN)₄]^{2-} (Ni²⁺, 3d⁸)**:
- Configuration: t₂g⁶ e₂ (all paired) → **Diamagnetic**
- **[Co(CN)₆]^{3-} (Co³⁺, 3d⁶)**:
- Configuration: t₂g⁶ e₀ (all paired) → **Diamagnetic**

5. **Count the number of paramagnetic complexes:**
- From the analysis:
- **Paramagnetic complexes**: `[Fe(CN)₆]^{3-}` and `[Ti(CN)₆]^{3-}`
- **Diamagnetic complexes**: `[Fe(CN)₆]^{4-}`, `[Ni(CN)₄]^{2-}`, and `[Co(CN)₆]^{3-}`

### Conclusion:
The total number of paramagnetic complexes is **2**.

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