1. Identify the type of isomerism in each pair

We check whether both complexes in a given option exhibit the same kind of isomerism.

Option A

Given:

• $[Cr(NH_3)_5Cl]Cl_2$
• $[Cr(NH_3)_4Cl_2]Cl$

These are two different compounds with different numbers of coordinated and ionisable chloride ions.

• In $[Cr(NH_3)_5Cl]Cl_2$, one $Cl^-$ is inside the coordination sphere and two are outside.
• In $[Cr(NH_3)_4Cl_2]Cl$, two $Cl^-$ are inside and one is outside.

This suggests ionisation isomerism / hydrate-like exchange idea is not applicable between these two as a pair of isomers, because the ligand composition inside the coordination sphere is different and they are not a standard isomeric pair of the same formula. Also, considering individual complexes:

• $[Cr(NH_3)_5Cl]^{2+}$ is octahedral of type $[MA_5B]$, so it shows no geometrical isomerism.
• $[Cr(NH_3)_4Cl_2]^+$ is octahedral of type $[MA_4B_2]$, so it shows geometrical isomerism (cis/trans).

Thus they do not exhibit the same kind of isomerism.

Option A: Incorrect

Option B

Given:

• $[Co(NH_3)_4Cl_2]^+$
• $[Pt(NH_3)_2(H_2O)Cl]^+$

First complex: $[Co(NH_3)_4Cl_2]^+$

This is octahedral, type $[MA_4B_2]$. It shows geometrical isomerism: cis and trans.

Second complex: $[Pt(NH_3)_2(H_2O)Cl]^+$

Platinum(II) is generally square planar. This is of type $[MA_2BC]$. Such square planar complexes also show geometrical isomerism.

Hence both exhibit geometrical isomerism.

Option B: Correct

Option C

Given:

• $[CoBr_2Cl_2]^{2-}$
• $[PtBr_2Cl_2]^{2-}$

First complex: $[CoBr_2Cl_2]^{2-}$

Here cobalt is tetrahedral in typical halide complexes of $Co^{2+}$. A tetrahedral complex of type $[MA_2B_2]$ does not show geometrical isomerism.

Second complex: $[PtBr_2Cl_2]^{2-}$

Platinum(II) is square planar. Square planar $[MA_2B_2]$ shows geometrical isomerism (cis/trans).

Thus the two do not exhibit the same kind of isomerism.

Option C: Incorrect

Option D

Given:

• $[Pt(NH_3)_3(NO_2)]Cl$
• $[Pt(NH_3)_3Cl]Br$

From the notation in the prompt, this option is intended as complexes of the type $[Pt(NH_3)_3X]Y$ with exchange between coordinated anion and counter anion. Such pairs are classic examples of ionisation isomerism.

For example, one form has $Cl^-$ coordinated and another has the other anion coordinated, leading to different ions in solution though same overall composition.

Thus this pair represents ionisation isomerism.

Option D: Correct

Final conclusion

The pairs exhibiting the same kind of isomerism are:

$\boxed{B,\ D}$

Comparison with stored answer

Stored correct answer: B, D

My derived answer matches the stored answer.