Total number of paramagnetic complexes which are inner orbital complexes :
`(i) [Cr(NH_(3))_(6)]Cl_(3) " " (ii)[Co(NH_(3))_(6)](NO_(3))_(2)" " (iii)[Ni(NH_(3))_(6)]SO_(4)`
`(iv) K_(2)[PtCl_(6)]. " " (v) [V(H_(2)O)_(6)]SO_(4) " " (vi) [Mn(NH_(3))_(6)]SO_(4)`
`(vii)[Fe(H_(2)O)_(5)(NO)]SO_(4) " " (viii)K_(3)[CuCl_(4)]" " Na_(4)[Fe(CN)_(5)(NOS)]`

Answer

To determine the total number of paramagnetic complexes that are inner orbital complexes from the given list, we will analyze each complex step by step.

### Step 1: Analyze Each Complex
1. **Complex (i): [Cr(NH₃)₆]Cl₃**
- Oxidation state of Cr: +3
- Electron configuration: Cr³⁺ (d³)
- Hybridization: d²sp³ (inner orbital complex)
- Paramagnetic: Yes (unpaired electrons)
- **Conclusion**: Inner orbital and paramagnetic.

2. **Complex (ii): [Co(NH₃)₆](NO₃)₂**
- Oxidation state of Co: +2
- Electron configuration: Co²⁺ (d⁷)
- Hybridization: sp³d² (outer orbital complex)
- Paramagnetic: Yes (unpaired electrons)
- **Conclusion**: Not an inner orbital complex.

3. **Complex (iii): [Ni(NH₃)₆]SO₄**
- Oxidation state of Ni: +2
- Electron configuration: Ni²⁺ (d⁸)
- Hybridization: sp³d² (outer orbital complex)
- Paramagnetic: Yes (unpaired electrons)
- **Conclusion**: Not an inner orbital complex.

4. **Complex (iv): K₂[PtCl₆]**
- Oxidation state of Pt: +4
- Electron configuration: Pt⁴⁺ (d⁶)
- Hybridization: d²sp³ (inner orbital complex)
- Paramagnetic: No (all electrons paired)
- **Conclusion**: Not paramagnetic.

5. **Complex (v): [V(H₂O)₆]SO₄**
- Oxidation state of V: +2
- Electron configuration: V²⁺ (d³)
- Hybridization: d²sp³ (inner orbital complex)
- Paramagnetic: Yes (unpaired electrons)
- **Conclusion**: Inner orbital and paramagnetic.

6. **Complex (vi): [Mn(NH₃)₆]SO₄**
- Oxidation state of Mn: +2
- Electron configuration: Mn²⁺ (d⁵)
- Hybridization: sp³d² (outer orbital complex)
- Paramagnetic: Yes (unpaired electrons)
- **Conclusion**: Not an inner orbital complex.

7. **Complex (vii): [Fe(H₂O)₅(NO)]SO₄**
- Oxidation state of Fe: +3
- Electron configuration: Fe³⁺ (d⁵)
- Hybridization: sp³d² (outer orbital complex)
- Paramagnetic: Yes (unpaired electrons)
- **Conclusion**: Not an inner orbital complex.

8. **Complex (viii): K₃[CuCl₄]**
- Oxidation state of Cu: +1
- Electron configuration: Cu¹⁺ (d¹⁰)
- Hybridization: sp³ (outer orbital complex)
- Paramagnetic: No (all electrons paired)
- **Conclusion**: Not paramagnetic.

9. **Complex (ix): Na₄[Fe(CN)₅(NO)]**
- Oxidation state of Fe: +2
- Electron configuration: Fe²⁺ (d⁶)
- Hybridization: d²sp³ (inner orbital complex)
- Paramagnetic: No (all electrons paired due to strong field ligands)
- **Conclusion**: Not paramagnetic.

### Step 2: Count the Paramagnetic Inner Orbital Complexes
From the analysis:
- Complex (i): [Cr(NH₃)₆]Cl₃ - Inner orbital, paramagnetic.
- Complex (v): [V(H₂O)₆]SO₄ - Inner orbital, paramagnetic.

### Final Answer
The total number of paramagnetic complexes that are inner orbital complexes is **2**.