Total number of complexes among the following which are opticaly active?
(i) `[Cr(O x)_(3)]^(3-)`
(ii) cis-`[Pt(Cl_(2))(en)]`
(iii) cis`[Rh(Cl_(2))(NH_(3))_(4)]^(+)`
(iv) `Ru(dipy)_(3)]^(3+)`
(v) cis`[Co(NO_(2))_(3)(dien)]`
(vi) Trans-`[Co(NO_(2))_(3)(dien)]`
(vii) cis`[Co(NO_(2))_(3)(NH_(3))_(3)]`

Answer

To determine the total number of complexes that are optically active among the given options, we will analyze each complex one by one. A complex is optically active if it has non-superimposable mirror images, meaning it lacks a plane of symmetry.

### Step-by-Step Solution:

1. **Complex (i): `[Cr(Ox)₃]³⁻`**
- The oxalate ion (Ox) is a bidentate ligand. The complex has an octahedral geometry.
- Since the arrangement of the oxalate ligands can create a non-superimposable mirror image, this complex is optically active.

2. **Complex (ii): `cis-[Pt(Cl₂)(en)]`**
- The ethylenediamine (en) is a bidentate ligand, and there are two chloride ligands.
- In the cis configuration, the two chloride ions are adjacent. The presence of identical ligands leads to a plane of symmetry, making this complex optically inactive.

3. **Complex (iii): `cis-[Rh(Cl₂)(NH₃)₄]⁺`**
- This complex also has an octahedral geometry with two identical chloride ligands and four ammonia ligands.
- Similar to the previous case, the identical ligands create a plane of symmetry, rendering this complex optically inactive.

4. **Complex (iv): `[Ru(dipy)₃]³⁺`**
- Dipyridine (dipy) is a bidentate ligand. The complex has an octahedral geometry with three dipyridine ligands.
- The arrangement of the dipyridine ligands leads to a non-superimposable mirror image, making this complex optically active.

5. **Complex (v): `cis-[Co(NO₂)₃(dien)]`**
- The diethylenetriamine (dien) is a tridentate ligand, and there are three nitro ligands.
- The presence of the symmetrical tridentate ligand and identical nitro ligands creates a plane of symmetry, making this complex optically inactive.

6. **Complex (vi): `trans-[Co(NO₂)₃(dien)]`**
- Similar to the previous case, the trans configuration also leads to symmetry due to the arrangement of ligands.
- Therefore, this complex is also optically inactive.

7. **Complex (vii): `cis-[Co(NO₂)₃(NH₃)₃]`**
- This complex has three nitro ligands and three ammonia ligands.
- The arrangement of identical ligands leads to a symmetrical structure, making this complex optically inactive.

### Summary of Optical Activity:
- **Optically Active Complexes:** (i) `[Cr(Ox)₃]³⁻` and (iv) `[Ru(dipy)₃]³⁺`
- **Total Number of Optically Active Complexes:** 2

### Final Answer:
The total number of complexes that are optically active is **2**.