Which of the following cannot be represented by resonance structures?

Resonance refers to the delocalisation of $$\pi$$-electrons (and lone-pair electrons that can convert to $$\pi$$-electrons) over two or more adjacent, coplanar, conjugated atoms. A molecule or ion will show resonance only if such a continuous conjugated system exists.
The key checkpoints are:
- At least one $$\pi$$-bond or an adjacent lone pair in an orbital that can overlap sideways.
- Continuous overlap of $$p$$ orbitals over three or more atoms.

Now examine every option.

Option A Dimethyl ether, $$CH_3-O-CH_3$$
The central oxygen possesses two lone pairs, but both adjacent atoms are sp3-hybridised carbons that contain only $$\sigma$$ bonds. No adjacent empty or partially filled $$p$$ orbital is present, so the lone pairs on oxygen cannot delocalise. Hence no alternative Lewis (resonance) structures are possible. Therefore dimethyl ether cannot be represented by resonance structures.

Option B Nitrate anion, $$NO_3^-$$
The nitrogen is $$sp^2$$-hybridised and each oxygen carries either a $$\pi$$ bond or a lone pair that can participate in $$p$$-orbital overlap. This gives three equivalent Lewis structures obtained by shifting the $$N$$=O double bond and negative charge around the three oxygens. Hence nitrate ion definitely exhibits resonance.

Option C Carboxylate anion, $$RCOO^-$$
A carboxylate ion has two oxygen atoms bonded to the same carbon; the negative charge and the $$\pi$$ bond can be interchanged between the two oxygens, giving two equivalent resonance structures. So the carboxylate anion is resonating.

Option D Toluene, $$C_6H_5CH_3$$
The benzene ring itself contains a conjugated $$\pi$$ system with six electrons shared over six carbon atoms, represented by two Kekulé resonance forms (and additional Dewar forms). Thus toluene also possesses resonance.

Among the four, the only species lacking any conjugated $$\pi$$ system is dimethyl ether. Hence it cannot be represented by resonance structures.

Final answer: Option A which is: Dimethyl ether