1. Check statement A: “The strength of anionic ligands can be explained by crystal field theory.”

   This statement is false.

   • Crystal Field Theory (CFT) explains splitting of $d$-orbitals due to electrostatic interaction between metal ion and ligands.
   • However, the relative ligand strength (spectrochemical series), especially why some ligands are strong-field and others weak-field, is not fully explained by simple CFT.
   • For this, more advanced theories like Ligand Field Theory / Molecular Orbital Theory are needed.

   Hence, A is incorrect.

2. Check statement B: “Valence bond theory does not give a quantitative interpretation of kinetic stability of coordination compounds.”

   This statement is true.

   • Valence Bond Theory (VBT) explains geometry and magnetic behavior qualitatively.
   • It does not explain kinetic stability/inertness vs lability quantitatively.
   • In fact, VBT has important limitations in discussing rates of ligand substitution.

   Hence, B is correct.

3. Check statement C: “The hybridization involved in formation of $[\mathrm{Ni}(\mathrm{CN})_4]^{2-}$ complex is $\mathrm{dsp}^2$.”

   This statement is true.

   • Oxidation state of Ni: $x+4(-1)=-2 \Rightarrow x=+2$
   • So metal ion is $\mathrm{Ni}^{2+}$.
   • Electronic configuration of $\mathrm{Ni}^{2+}$: $[\mathrm{Ar}]3d^8$
   • $\mathrm{CN}^-$ is a strong-field ligand, so electrons pair up.
   • For coordination number 4 with strong-field $d^8$ metal, the complex becomes square planar.
   • Square planar complexes involve $dsp^2$ hybridization.

   Hence, C is correct.

4. Check statement D: “The number of possible isomer(s) of cis-$[\mathrm{PtCl}_2(\mathrm{en})_2]^{2+}$ is one.”

   This statement is false.

   • Here, $\mathrm{en}$ is ethylenediamine, a bidentate ligand.
   • The complex is octahedral: $[\mathrm{PtCl}_2(\mathrm{en})_2]^{2+}$.
   • For octahedral complexes of type $[M(AA)_2X_2]$, the cis form is optically active and exists as two enantiomers ($\Delta$ and $\Lambda$).
   • Therefore, cis-$[\mathrm{PtCl}_2(\mathrm{en})_2]^{2+}$ has 2 isomers, not 1.

   Hence, D is incorrect.

5. Identify correct statements

   Correct statements are: $\boxed{B \text{ and } C}$

6. Match with options

   • Option A: B, C only ✔
   • Option B: B, D only ✘
   • Option C: A, C only ✘
   • Option D: A, D only ✘

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