Analyze Statement I

We examine both complexes mentioned.

(a) $[Ni(CN)_4]^{2-}$

• Oxidation state of Ni: $x + 4(-1) = -2 \implies x = +2$
• So, $Ni^{2+}$ has configuration: $Ni: [Ar]3d^8 4s^2 \Rightarrow Ni^{2+}: [Ar]3d^8$
• $CN^-$ is a strong field ligand, so pairing occurs.
• For $d^8$ with strong field in coordination number 4, the complex becomes square planar with $dsp^2$ hybridization.
• All electrons are paired, so it is diamagnetic.

Hence this part is correct.

(b) $[Ni(CO)_4]$

• CO is a neutral ligand, so oxidation state of Ni is $0$.
• Configuration of $Ni^0$: $[Ar]3d^8 4s^2$
• In $[Ni(CO)_4]$, nickel uses $sp^3$ hybridization and forms a tetrahedral complex.
• All electrons become paired in the metal-ligand bonding situation, so $[Ni(CO)_4]$ is diamagnetic, not paramagnetic.

Therefore, Statement I says "$[Ni(CO)_4]$ is tetrahedral, paramagnetic and with $sp^3$ hybridization".

• Tetrahedral: true
• $sp^3$: true
• Paramagnetic: false

So Statement I is false.

Analyze Statement II

Statement II says: $[NiCl_4]^{2-}$ and $[Ni(CO)_4]$ both have same $d$-electron configuration, same geometry and are paramagnetic.

(a) $[NiCl_4]^{2-}$

• Oxidation state of Ni: $x + 4(-1) = -2 \implies x = +2$
• So, $Ni^{2+}$ is $3d^8$.
• $Cl^-$ is a weak field ligand, so no pairing occurs.
• Hence the complex is tetrahedral and paramagnetic.

(b) $[Ni(CO)_4]$

• Ni oxidation state is $0$.
• Thus it is not $d^8$ in the same sense as $Ni^{2+}$; the metal is $Ni^0$ with valence configuration $3d^8 4s^2$.
• Geometry is tetrahedral.
• But it is diamagnetic, not paramagnetic.

So in Statement II:

• same geometry: true
• same $d$-electron configuration: commonly treated as not same oxidation-state electronic situation; in standard coordination chemistry comparison, $[NiCl_4]^{2-}$ has $Ni^{2+}(d^8)$ while $[Ni(CO)_4]$ has $Ni^0$
• both paramagnetic: false

Therefore Statement II is false.

Final conclusion

• Statement I: False
• Statement II: False

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

Comparison with stored answer

Stored correct answer: B

My derived answer matches the stored answer.