The decreasing order of reactivity of the following organic molecules towards AgNO₃ solution is :

Solution

Chemistry ma’am · 4 steps

AgNO₃ pulls off Cl⁻, so rank these by how stable the carbocation left behind is.

1. What AgNO3 does. Ag⁺ grabs the chloride and AgCl precipitates, leaving a carbocation. This is an S_N1-type reaction, so the more stable the carbocation, the faster the precipitate forms.
2. Aromatic cation. Removing Cl⁻ from (A) gives the cyclopropenyl cation. It is planar and cyclic with 2 π electrons, which fits 4n + 2 with n = 0. So it is aromatic and very stable.

   Compound	Carbocation formed	Extra effect	Stability
   (B)	aromatic cyclopropenyl	OCH₃ donates a lone pair (+M)	highest
   (A)	aromatic cyclopropenyl	none	very high
   (C)	secondary, (CH₃)₂CH⁺	two methyls donate (+I, hyperconjugation)	moderate
   (D)	secondary	CH₂NO₂ withdraws (−I)	lowest

3. Compare the pairs. (B) has the same aromatic ring as (A), and the OCH₃ on the ring pushes electron density into the positive charge, so (B) beats (A). (C) and (D) are both secondary, but the NO₂ group in (D) pulls electrons away and destabilises the cation.
4. So. The order of reactivity is (B) > (A) > (C) > (D), option (a).

The idea to keep. Reactivity with AgNO₃ means carbocation stability. Aromaticity beats everything, electron donors push it higher, and electron-withdrawing groups like NO₂ pull it down.

Answer from the NTA final answer key. Solution by PrepWiser.