Identify the two complexes

We are comparing: $[\mathrm{NiCl_2Br_2}]^{2-}$ with $[\mathrm{PtCl_2Br_2}]^{2-}$

In both, the oxidation state of the metal is $+2$.

Electronic configurations of the metal ions

• $\mathrm{Ni}^{2+}$: $\mathrm{Ni} = [Ar]3d^84s^2 \Rightarrow \mathrm{Ni}^{2+} = [Ar]3d^8$
• $\mathrm{Pt}^{2+}$: $\mathrm{Pt} \approx [Xe]4f^{14}5d^96s^1 \Rightarrow \mathrm{Pt}^{2+} = 5d^8$

So both are $d^8$, but one is a 3d ion and the other is a 5d ion.

Geometry of the complexes

Both complexes are 4-coordinate.

• For $\mathrm{Ni}^{2+}$ (3d$^8$) with halide ligands, tetrahedral geometry is generally preferred: $[\mathrm{NiCl_2Br_2}]^{2-} \text{ is tetrahedral}$

• For $\mathrm{Pt}^{2+}$ (5d$^8$), square planar geometry is strongly preferred: $[\mathrm{PtCl_2Br_2}]^{2-} \text{ is square planar}$

Therefore, geometry changes.

So, A is correct.

Geometrical isomerism

• In a tetrahedral complex of type $[M A_2 B_2]$, all positions are equivalent, so no geometrical isomerism exists.
• In a square planar complex of type $[M A_2 B_2]$, cis and trans isomers are possible.

Hence:

• $[\mathrm{NiCl_2Br_2}]^{2-}$: no geometrical isomerism
• $[\mathrm{PtCl_2Br_2}]^{2-}$: shows geometrical isomerism

Therefore, geometrical isomerism changes.

So, B is correct.

Optical isomerism

Check both geometries:

• Tetrahedral $[M A_2 B_2]$ is not optically active.
• Square planar $[M A_2 B_2]$ is also not optically active.

Therefore, there is no change in optical isomerism.

So, C is not correct.

Magnetic properties

• Tetrahedral $\mathrm{Ni}^{2+}$ ($d^8$) is usually high spin with 2 unpaired electrons, so it is paramagnetic.
• Square planar $\mathrm{Pt}^{2+}$ ($d^8$) is low spin, all electrons paired, so it is diamagnetic.

Therefore, magnetic property changes.

So, D is correct.

Final evaluation of statements

• A. Geometry $\to$ changes
• B. Geometrical isomerism $\to$ changes
• C. Optical isomerism $\to$ does not change
• D. Magnetic properties $\to$ change

Hence the correct set is: $\boxed{A, B \text{ and } D}$

This corresponds to Option B.