The decreasing order of ease of alkaline hydrolysis for the following esters is:

Alkaline hydrolysis of ester follow $$SN_2$$ mechanism.

Alkaline hydrolysis of an ester proceeds via a nucleophilic acyl substitution ($$\text{B}_{\text{Ac}}2$$) mechanism. The rate-determining step involves the attack of the hydroxide nucleophile ($$\text{OH}^\ominus$$) on the electrophilic carbonyl carbon:

$$\text{Rate of Hydrolysis} \propto \text{Electrophilicity of the Carbonyl Carbon}$$

• Electron-Withdrawing Groups (EWGs) increase the positive charge density on the carbonyl carbon, making it more electrophilic and accelerating the rate of hydrolysis.
• Electron-Donating Groups (EDGs) decrease the positive charge density on the carbonyl carbon, stabilizing the ester starting material and slowing down the reaction.

Substituent Breakdown and Comparison:

1. Compound III ($$\text{--NO}_2$$ at para position):

   The nitro group is a very strong electron-withdrawing group via both resonance ($$\text{--R}$$) and inductive ($$\text{--I}$$) effects. This creates the highest positive charge on the carbonyl carbon, making III the most reactive.

2. Compound II ($$\text{--Cl}$$ at para position):

   The chlorine atom acts as an electron-withdrawing group primarily through its inductive ($$\text{--I}$$) effect, which outweighs its weak resonance donation. It increases the reactivity compared to the unsubstituted ester, but less than the nitro group.

3. Compound I (Unsubstituted Benzene Ring, $$\text{--H}$$):

   The unsubstituted ester serves as the standard baseline reference with no additional electronic enhancement or attenuation.

4. Compound IV ($$\text{--OCH}_3$$ at para position):

   The methoxy group is a powerful electron-donating group due to resonance ($$\text{+R}$$) from the lone pairs on the oxygen atom. This severely reduces the electrophilicity of the carbonyl carbon, making IV the least reactive.

Why Other Arrangements Are Incorrect:

• Any order placing IV anywhere but the last position is incorrect because strong resonance electron-donation ($$\text{+R}$$) always exhibits the lowest rate of nucleophilic attack.
• Any choice ranking II above III is incorrect because inductive withdrawal ($$\text{--I}$$) from a halogen is significantly weaker than the combined resonance ($$\text{--R}$$) and inductive withdrawal of a nitro group.

Conclusion:

Combining these trends gives the clear decreasing sequence of reactivity: III > II > I > IV.

Answer: Option B — III > II > I > IV