1. Identify the complex and its geometry

The complex ion is $[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]^+$ where $\mathrm{en}$ = ethylenediamine, a bidentate ligand.

Since there are two $\mathrm{en}$ ligands and two $\mathrm{Cl}^-$ ligands, cobalt has coordination number: $2\times 2 + 2\times 1 = 6$ So the complex is octahedral.

Thus, Reason (R) is correct.

2. Find the geometrical isomers of $[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]^+$

For an octahedral complex of type: $[M(AA)_2X_2]$ where $AA$ is a symmetric bidentate ligand like en, there are only two geometrical isomers:

• cis: the two $\mathrm{Cl}$ ligands are adjacent
• trans: the two $\mathrm{Cl}$ ligands are opposite

So the number of geometrical isomers is: $2$ not 3.

Hence, Assertion (A) is incorrect.

3. Why confusion may arise

The cis form of $[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]^+$ is optically active and exists as two enantiomers ($\Delta$ and $\Lambda$), while the trans form is optically inactive.

So total stereoisomers are:

• 2 optical isomers from cis
• 1 trans form

Thus, total stereoisomers = 3.

But the question asks specifically for geometrical isomers, not stereoisomers. Therefore geometrical isomers are only 2.

4. Evaluate the statements

• Assertion (A): "The total number of geometrical isomers shown by $[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]^+$ complex ion is three."
  False

• Reason (R): "$[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]^+$ complex ion has an octahedral geometry."
  True

Therefore, the correct option is: $\boxed{\text{B}}$

5. Comparison with stored answer

Stored correct answer: B
Derived answer: B

They agree.