Which of the following octahedral complex does not show geometrical isomerism (`A` and `B` are monodentate ligands) ?

Options

A. `[MA_(4)B_(2)]`
B. `[MA_(5)B]`
C. `[MA_(2)B_(4)]`
D. `[MA_(3)B_(3)]`

Answer

To determine which octahedral complex does not show geometrical isomerism, we need to analyze each of the given complexes based on their ligand arrangements.

### Step-by-Step Solution:

1. **Understanding Geometrical Isomerism**:
- Geometrical isomerism occurs in coordination compounds when ligands can be arranged differently around the central metal ion, leading to different spatial arrangements (cis and trans forms).

2. **Analyzing the First Complex (MA4B2)**:
- In this complex, we have 4 ligands A and 2 ligands B.
- The possible arrangements can lead to cis (where similar ligands are adjacent) and trans (where similar ligands are opposite each other) isomers.
- Thus, MA4B2 can show geometrical isomerism.

3. **Analyzing the Second Complex (MA5B)**:
- This complex consists of 5 ligands A and 1 ligand B.
- Since 5 out of 6 ligands are identical (A), there is no way to arrange the ligands to create distinct isomers.
- Therefore, MA5B does not show geometrical isomerism.

4. **Analyzing the Third Complex (MA2B4)**:
- Similar to the first complex, this one has 2 ligands A and 4 ligands B.
- It can also arrange itself in a way that allows for cis and trans isomers.
- Hence, MA2B4 can show geometrical isomerism.

5. **Analyzing the Fourth Complex (MA3B3)**:
- This complex has 3 ligands A and 3 ligands B.
- It can exhibit facial (fac) and meridional (mer) isomerism, which are types of geometrical isomerism.
- Therefore, MA3B3 does show geometrical isomerism.

### Conclusion:
After analyzing all the complexes, the only one that does not show geometrical isomerism is **MA5B**.

### Final Answer:
The octahedral complex that does not show geometrical isomerism is **MA5B**.