Meaning of ambidentate ligand

An ambidentate ligand is a ligand that can coordinate to the central metal atom through two different atoms, but only one at a time.

Examples:

• $\mathrm{NO_2^-}$: can bind through $N$ (nitro) or $O$ (nitrito)
• $\mathrm{NCS^-}$: can bind through $N$ or $S$

Check the ligands appearing in the options

• $\mathrm{C_2O_4^{2-}}$ (oxalate): bidentate, but not ambidentate in standard JEE classification. It coordinates through oxygen atoms as a chelating ligand.
• Ethylenediamine (en): bidentate, not ambidentate.
• $\mathrm{H_2O}$: monodentate, not ambidentate.
• $\mathrm{NO_2^-}$: ambidentate.
• $\mathrm{NCS^-}$: ambidentate.
• $\mathrm{EDTA^{4-}}$: hexadentate, not ambidentate.

Evaluate each option

Option A: $\mathrm{C_2O_4^{2-}},\ \mathrm{NO_2^-},\ \mathrm{NCS^-}$

• Contains $\mathrm{NO_2^-}$ and $\mathrm{NCS^-}$, both ambidentate.
• So this set has ambidentate ligand(s).

Option B: $\mathrm{C_2O_4^{2-}}$, ethylenediamine, $\mathrm{H_2O}$

• Oxalate: not ambidentate
• Ethylenediamine: not ambidentate
• Water: not ambidentate
• So this set does not have ambidentate ligand(s).

Option C: $\mathrm{NO_2^-},\ \mathrm{C_2O_4^{2-}},\ \mathrm{EDTA^{4-}}$

• Contains $\mathrm{NO_2^-}$, which is ambidentate.
• So this set has ambidentate ligand(s).

Option D: $\mathrm{EDTA^{4-}},\ \mathrm{NCS^-},\ \mathrm{C_2O_4^{2-}}$

• Contains $\mathrm{NCS^-}$, which is ambidentate.
• So this set has ambidentate ligand(s).

Conclusion

The only set which does not contain any ambidentate ligand is: $\boxed{\text{B}}$

Comparison with stored answer

Stored correct answer: B

My derived answer: B

Hence, they agree.