Read the paragraph carefully and answer the questions given below it,
Stereo//space isomerism in coordination compounds
Gcometrical isomerism: Exhibited by square planer and octahedral complexes (not by tetrahedral complexes because relative positions are similar). If opposite positions have similar groups, it is trans, otherwise it is cis,
Optical isomerism: Shown when mirror image is non-superimposable. Cis-isomer shows but trans isomer does not
QWhich of the following types of octahedral complexes will exhibit geometrical isomerism (where M = metal and a, b are achiral ligands)

Options

A. `[Ma_(6)]`
B. `[Ma_(3)b]`
C. `[Ma_(4)b_(2)]`
D. `[Mab_(3)]`

Answer

To solve the question regarding which types of octahedral complexes will exhibit geometrical isomerism, we will analyze the given options based on the principles of geometrical isomerism in coordination compounds.

### Step-by-Step Solution:

1. **Understanding Geometrical Isomerism**:
- Geometrical isomerism occurs in coordination compounds when the ligands can occupy different positions around the central metal atom. For octahedral complexes, this typically involves the arrangement of ligands in either a cis or trans configuration.

2. **Analyzing the Options**:
- We have four options to consider: \( \text{MA}_6 \), \( \text{MA}_3\text{B} \), \( \text{MA}_4\text{B}_2 \), and \( \text{MA}\text{B}_3 \).

3. **Option A: \( \text{MA}_6 \)**:
- In this complex, all six ligands are identical (A). Since there are no different ligands to create distinct arrangements, \( \text{MA}_6 \) does not exhibit geometrical isomerism.

4. **Option B: \( \text{MA}_3\text{B} \)**:
- This complex has three identical ligands (A) and one different ligand (B). However, due to the symmetry of the octahedral structure, interchanging the positions of A and B does not create a new arrangement. Thus, \( \text{MA}_3\text{B} \) does not exhibit geometrical isomerism.

5. **Option C: \( \text{MA}_4\text{B}_2 \)**:
- In this complex, we have four identical ligands (A) and two identical ligands (B). The arrangement can lead to two geometrical isomers: one where the two B ligands are opposite each other (trans) and one where they are adjacent (cis). Therefore, \( \text{MA}_4\text{B}_2 \) does exhibit geometrical isomerism.

6. **Option D: \( \text{MA}\text{B}_3 \)**:
- Similar to option B, this complex has one A ligand and three B ligands. The symmetry of the octahedral structure means that this arrangement does not create distinct geometrical isomers. Thus, \( \text{MA}\text{B}_3 \) does not exhibit geometrical isomerism.

### Conclusion:
The only octahedral complex that exhibits geometrical isomerism is **Option C: \( \text{MA}_4\text{B}_2 \)**.