Give the ratio of trans- isomers is`[M(Aab_(2)c_(2)]`(A) and `[Ma_(4)b_(2)](B)` respectively .

Explanation

To determine the ratio of trans isomers in the coordination compounds [M(Aa2B2)] (A) and [M(A4B2)] (B), we need to analyze the structure of each complex and identify the possible trans isomers.

### Step-by-Step Solution:

1. **Identify the Ligands and Their Coordination**:
- For complex A: [M(Aa2B2)], we have:
- M: Metal
- Aa: Bidentate ligand (can bind at two sites)
- B: Unidentate ligand (binds at one site)
- For complex B: [M(A4B2)], we have:
- M: Metal
- A: Unidentate ligand (binds at one site)
- B: Unidentate ligand (binds at one site)

2. **Determine the Possible Trans Isomers for Complex A**:
- In [M(Aa2B2)], the bidentate ligand Aa can occupy two coordination sites, leading to different arrangements with the unidentate ligands B.
- The two possible trans isomers can be visualized as:
- Isomer 1: B and B in trans positions with respect to the bidentate ligand Aa.
- Isomer 2: One B and one C in trans positions with respect to the bidentate ligand Aa.
- Therefore, there are **2 trans isomers** for complex A.

3. **Determine the Possible Trans Isomers for Complex B**:
- In [M(A4B2)], we have four A ligands and two B ligands.
- The arrangement can be visualized with B ligands occupying axial positions and A ligands occupying equatorial positions.
- Since all A ligands are identical and the B ligands are also identical, there is only **1 trans isomer** for complex B.

4. **Calculate the Ratio of Trans Isomers**:
- From the analysis, we have:
- Trans isomers in complex A: 2
- Trans isomers in complex B: 1
- Thus, the ratio of trans isomers in [M(Aa2B2)] to [M(A4B2)] is:
\[ \text{Ratio} = \frac{2}{1} = 2:1 \]

### Final Answer:
The ratio of trans isomers in [M(Aa2B2)] and [M(A4B2)] is **2:1**.