Key idea: origin of colour in aqueous solutions of transition-metal salts

A compound gives a coloured aqueous solution if the dissolved metal ion in water has partially filled $d$-orbitals, so that $d$-$d$ transitions are possible.

Also, the question specifies nitrogen atmosphere, which means we should ignore oxidation by air/oxygen.

Check each option

Option A: $CuCl_2$

On dissolving in water: $CuCl_2 \rightarrow Cu^{2+} + 2Cl^-$ In water, $Cu^{2+}$ forms hydrated ions like $[Cu(H_2O)_6]^{2+}$.

Electronic configuration of $Cu^{2+}$: $Cu: [Ar]3d^{10}4s^1$ $Cu^{2+}: [Ar]3d^9$

Since it has incompletely filled $d$-orbitals ($3d^9$), its aqueous solution is coloured (blue/blue-green).

So, A gives a coloured solution.

Option B: $AgCl$

$AgCl$ is insoluble/sparingly soluble in water, so it does not appreciably give an aqueous ionic solution.

Even if considered, $Ag^+$ has configuration: $Ag: [Kr]4d^{10}5s^1$ $Ag^+: [Kr]4d^{10}$

A $d^{10}$ ion is generally colourless.

So, B does not give a coloured solution.

Option C: $ZnCl_2$

On dissolving: $ZnCl_2 \rightarrow Zn^{2+} + 2Cl^-$

Electronic configuration of $Zn^{2+}$: $Zn: [Ar]3d^{10}4s^2$ $Zn^{2+}: [Ar]3d^{10}$

Since $Zn^{2+}$ is $d^{10}$, its aqueous solution is colourless.

So, C is not correct.

Option D: $Cu_2Cl_2$

This is cuprous chloride, i.e. $CuCl$, containing $Cu^+$.

On dissolving (conceptually): $Cu^+$ Electronic configuration: $Cu^+: [Ar]3d^{10}$

A $d^{10}$ ion is colourless. Also, in nitrogen atmosphere we avoid oxidation of $Cu^+$ to $Cu^{2+}$ by air, so we should consider $Cu^+$ itself.

Therefore, D does not give a coloured solution in nitrogen atmosphere.

Conclusion

The only compound that gives a coloured solution in water under nitrogen atmosphere is: $\boxed{A\; (CuCl_2)}$

Comparison with stored answer

Stored correct answer: A

My derived answer: A

Hence, they agree.