An isomerr of the complex `CoBrCl_(2)(en)_(2)(H_(2)O)`, on reaction with concentrated `H_(2)SO_(4)` (dehydrating agent), suffers no loss in weight and on reaction with `AgNO_(3)` solution it gives only white precipitate, which is soluble in `NH_(3)` solution.
Q. The incorrect statement about complex is:

Options

A. It can show geometrical isomerism
B. cis isomer is optically active
C. Trans isomer is optically active
D. it can exhibit solvate isomerism

Explanation

To solve the question regarding the complex `CoBrCl₂(en)₂(H₂O)`, we need to analyze the information provided and determine which statement about the complex is incorrect.

### Step-by-Step Solution:

1. **Understanding the Complex**: The complex given is `CoBrCl₂(en)₂(H₂O)`. Here, `en` stands for ethylenediamine, which is a bidentate ligand. The complex contains cobalt as the central metal ion, bromide (Br⁻), chloride (Cl⁻), ethylenediamine ligands, and a water molecule (H₂O).

2. **Reaction with Concentrated H₂SO₄**: The complex reacts with concentrated sulfuric acid (H₂SO₄), which is a dehydrating agent. The fact that it suffers no loss in weight indicates that the water molecule (H₂O) is likely coordinated to the cobalt ion. If it were not coordinated, it would be lost during the reaction, resulting in a loss of weight.

3. **Reaction with AgNO₃**: When the complex reacts with silver nitrate (AgNO₃), it produces a white precipitate. The white precipitate can be due to the formation of silver chloride (AgCl), which is known to be a white solid. The fact that this precipitate is soluble in ammonia (NH₃) suggests that the chloride ion is outside the coordination sphere, as AgCl dissolves in ammonia to form a complex.

4. **Geometrical Isomerism**: The complex can exhibit geometrical isomerism due to the presence of two different types of ligands (Br and Cl) and the bidentate nature of `en`. This allows for cis and trans isomers to exist.

5. **Optical Activity**: The cis isomer of the complex is optically active because it lacks a plane of symmetry, while the trans isomer is optically inactive due to the presence of a plane of symmetry.

6. **Identifying Incorrect Statement**: Now, we need to identify the incorrect statement about the complex:
- **Statement 1**: It can show geometrical isomerism. (Correct)
- **Statement 2**: The cis isomer is optically active. (Correct)
- **Statement 3**: The trans isomer is optically active. (Incorrect)
- **Statement 4**: It can show solvate isomerism. (Correct)

### Conclusion:
The incorrect statement about the complex is that the trans isomer is optically active. Therefore, the answer is **Statement 3**.