Core Logic
The stability of arenediazonium salts is dictated by the ability of substituents on the benzene ring to disperse the positive charge on the diazonium group (-N₂^+$\mathrm{-N_2^+}$).
Electron-donating groups (EDG) increase the stability by resonance (+M effect) and inductive (+I) effects, dispersing the positive charge.
Electron-withdrawing groups (EWG) decrease the stability by intensifying the positive charge (-M, -I effects).
Let's evaluate the given substituents at the para position:
(A) -OCH₃$\mathrm{-OCH_3}$: Strong +M effect. Highly stabilizing.
(C) Plain benzene ring: Neutral baseline.
(D) -CN$\mathrm{-CN}$: Strong -M and -I effect. Destabilizing.
(B) -NO₂$\mathrm{-NO_2}$: Very strong -M and -I effect. Most destabilizing.
Step 1: Final Conclusion
Arranging them in decreasing order of stability:
(A) -OCH₃$\mathrm{-OCH_3}$ (+M$+M$) > (C) Baseline > (D) -CN$\mathrm{-CN}$ (-M$-M$) > (B) -NO₂$\mathrm{-NO_2}$ (Stronger -M$-M$).
Thus, the correct order is A > C > D > B$\text{A} > \text{C} > \text{D} > \text{B}$.
Pattern Recognition
Stability of carbocations and diazonium ions follows: +M > +I > no effect > -I > -M$+M > +I > \text{no effect} > -I > -M$. Look directly at the para group to rank.
Chapter Mix
Class 12 Chemistry: Amines
Class 11 Chemistry: Organic Chemistry - Some Basic Principles and Techniques