1. Identify the complex and its geometrical isomers

The complex is of the type $[M(NH_3)_4Cl_2]$ which is an octahedral complex of the form $[MA_4B_2]$.

Such complexes show two geometrical isomers:

• cis-$[M(NH_3)_4Cl_2]$
• trans-$[M(NH_3)_4Cl_2]$

2. Check Statement 1: Are the geometrical isomers optically inactive?

For octahedral complexes of the type $[MA_4B_2]$:

• the trans isomer is definitely optically inactive due to symmetry.
• the cis isomer is also optically inactive because it contains a plane of symmetry.

Hence, neither cis nor trans form is chiral.

So, Statement 1 is True.

3. Check Statement 2: Do both geometrical isomers possess an axis of symmetry?

We examine both isomers:

(i) trans-$[M(NH_3)_4Cl_2]$

This has a clear symmetry axis passing through the two opposite $Cl$ ligands and the metal center. So it possesses an axis of symmetry.

(ii) cis-$[M(NH_3)_4Cl_2]$

This also has a symmetry axis (a $C_2$ axis) in the octahedral arrangement.

Therefore, both geometrical isomers do possess an axis of symmetry.

So, Statement 2 is True.

4. Is Statement 2 the correct explanation of Statement 1?

Optical activity requires chirality, i.e. absence of improper symmetry elements such as:

• plane of symmetry,
• center of symmetry,
• etc.

Merely having an axis of symmetry does not by itself guarantee optical inactivity. Many chiral molecules can possess a proper rotation axis.

For this complex:

• the trans isomer is optically inactive mainly due to higher symmetry (including center/plane elements),
• the cis isomer is optically inactive because of a plane of symmetry, not simply because it has an axis of symmetry.

Thus, although Statement 2 is True, it is not the correct explanation of Statement 1.

5. Final option

• Statement 1: True
• Statement 2: True
• Statement 2 is not the correct explanation of Statement 1

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

6. Comparison with stored correct answer

Stored correct answer: B

My derived answer: B

So, they agree.