The most stable carbocation for the following is:

Solution

Chemistry ma’am · 3 steps

Walk the + charge around the ring and check whether it ever lands on the carbon holding NH₂.

1. Spread the charge. In each ion the C⁺ is conjugated with two ring double bonds, so the positive charge is shared by three alternate carbons. What decides stability is where the NH₂ group sits relative to those three carbons.
2. What NH2 can do. Nitrogen's lone pair helps only when the NH₂ is on a carbon that carries the + charge in some resonance form. Then it forms a C=N⁺ bond, and every atom has a full octet. Anywhere else, NH₂ gives only its electron-withdrawing -I effect, which destabilises the cation.

   C(+)-N̈H₂ ↔ C=N(+)H₂

   Ion	Where NH₂ sits	Lone pair reaches the + charge?	Net effect
   a	on the sp³ carbon, cut off from the π system	no	only -I, destabilised
   b	on the sp³ carbon, cut off from the π system	no	only -I, destabilised
   c	on a ring carbon that carries the + charge in one resonance form	yes, forms C=N⁺	strongly stabilised
   d	on a π carbon next to C⁺, but the charge never lands there	no	only -I, destabilised

3. So. Only in c can the nitrogen lone pair share the positive charge, so c is the most stable carbocation, which is option (c).

The idea to keep. A lone-pair donor stabilises a carbocation by resonance only if it is on a carbon where the + charge actually lands. Push the charge through every resonance form first, then check where the donor sits.

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