The incorrect statement is.

We begin by recalling the spin-only magnetic-moment formula. For any complex that has $$n$$ unpaired electrons, the spin-only magnetic moment is given by

$$\mu_{\text{spin}}=\sqrt{n(n+2)}\ \text{BM}.$$

Now let us examine every option one by one and verify each numerical or factual claim.

Option A speaks about the hexaaqua complexes $$[\,\text{Fe(H}_2\text O)_6\,]^{2+}$$ and $$[\,\text{Cr(H}_2\text O)_6\,]^{2+}$$.

• In $$\text{Fe}^{2+}$$ the electronic configuration is $$3d^6$$. Because $$\text H_2\text O$$ is a weak‐field ligand, the complex is high-spin, so the distribution is $$t_{2g}^4e_g^2$$ which contains $$4$$ unpaired electrons. Substituting $$n=4$$ in the formula gives

$$\mu=\sqrt{4(4+2)}=\sqrt{24}=4.90\ \text{BM}.$$

• In $$\text{Cr}^{2+}$$ the configuration is $$3d^4$$. With the same weak-field ligand, this also remains high-spin, giving $$t_{2g}^3e_g^1$$, again $$4$$ unpaired electrons. Therefore

$$\mu=\sqrt{4(4+2)}=\sqrt{24}=4.90\ \text{BM}.$$

The two values are equal, hence “nearly similar” is a correct statement.

Option B concerns $$[\,\text{Ni(NH}_3)_4\text{(H}_2\text O)_2\,]^{2+}$$. Here $$\text{Ni}^{2+}$$ is $$3d^8$$.

Both $$\text{NH}_3$$ and $$\text H_2\text O$$ are at best moderate to weak field ligands, so the octahedral complex remains high-spin: the configuration is $$t_{2g}^6e_g^2$$ which possesses $$2$$ unpaired electrons.

Putting $$n=2$$ in the formula gives

$$\mu=\sqrt{2(2+2)}=\sqrt{8}=2.83\ \text{BM}.$$

Hence the numerical value stated is correct.

Option C makes a mineralogical assertion: “The gemstone, ruby, has $$\text{Cr}^{3+}$$ ions occupying the octahedral sites of beryl.” The well-known facts are:

• Ruby is essentially corundum, i.e. crystalline $$\text{Al}_2\text{O}_3$$, in which a small fraction of the $$\text{Al}^{3+}$$ ions in the octahedral sites are replaced (doped) by $$\text{Cr}^{3+}$$ ions.

• Beryl, by contrast, is $$\text{Be}_3\text{Al}_2\text{Si}_6\text O_{18}$$ and when doped with $$\text{Cr}^{3+}$$ forms the green gemstone emerald, not ruby.

Therefore attributing ruby to beryl is factually wrong. This makes Option C incorrect.

Option D addresses the colour of $$[\,\text{CoCl(NH}_3)_5\,]^{2+}$$. Experimental observation shows that this complex appears violet-purple. According to complementary-colour principles, an observed violet colour implies that yellow light (its complement) is predominantly absorbed. Hence the option’s wording (“violet as it absorbs the yellow light”) is consistent with colour theory and is correct.

Summarising the analysis: Options A, B and D are correct, whereas Option C is wrong.

Hence, the correct answer is Option C.