A coordination complex of type `MX_(2)Y_(2)` (M-metal ion: X, Y-monodentate lingads), can have either a tetrahedral or a square planar geometry. The maximum number of posible isomers in these two cases are respectively:

Options

A. 1 and 2
B. 2 and 1
C. 1 and 3
D. 3 and 2

Explanation

To determine the maximum number of possible isomers for the coordination complex of type \( MX_2Y_2 \) (where \( M \) is the metal ion and \( X \) and \( Y \) are monodentate ligands), we need to analyze both tetrahedral and square planar geometries.

### Step 1: Analyze Tetrahedral Geometry
- In a tetrahedral complex, the arrangement of ligands around the central metal ion is such that all ligands are positioned at the corners of a tetrahedron.
- For the complex \( MX_2Y_2 \), there are two \( X \) ligands and two \( Y \) ligands.
- In tetrahedral geometry, there are no geometrical isomers because all ligands are adjacent to each other, and there is no way to rearrange them to create different spatial arrangements.
- Additionally, tetrahedral complexes do not exhibit optical isomerism due to the presence of a point of symmetry.

**Conclusion for Tetrahedral Geometry:**
- Maximum number of isomers: **1**

### Step 2: Analyze Square Planar Geometry
- In a square planar complex, the ligands are arranged in a square plane around the central metal ion.
- For the complex \( MX_2Y_2 \), we can have two geometrical isomers based on the arrangement of the \( X \) and \( Y \) ligands:
1. **Cis Isomer:** Both \( X \) ligands are adjacent to each other.
2. **Trans Isomer:** The \( X \) ligands are opposite each other.

- Similar to tetrahedral complexes, square planar complexes do not exhibit optical isomerism due to the presence of a plane of symmetry.

**Conclusion for Square Planar Geometry:**
- Maximum number of isomers: **2**

### Final Answer
- Therefore, the maximum number of possible isomers for the coordination complex \( MX_2Y_2 \) in tetrahedral geometry is **1**, and in square planar geometry is **2**.

### Summary:
- Maximum isomers in tetrahedral geometry: **1**
- Maximum isomers in square planar geometry: **2**