The cyclic cations having the same number of hyperconjugation are:

- A
A, C and D only
- B
A and B Only
- C
A and C Only
- D
B and C Only
The cyclic cations having the same number of hyperconjugation are:

A, C and D only
A and B Only
A and C Only
B and C Only
Correct answer:A
Standard Method
Given: Four cyclic carbocations A, B, C and D are shown.
Find: Which cations have the same number of hyperconjugative structures.
Principle: Hyperconjugation in a carbocation depends on the number of available -hydrogens on the carbon adjacent to the positively charged carbon. Each -hydrogen gives one hyperconjugative structure.
For A, the carbocation is adjacent to a CH group, so it has -hydrogens.
For B, the carbocation is adjacent to a CH group in the ring, so it has -hydrogens.
For C, the carbocation is adjacent to a CH group, so it again has -hydrogens.
For D, the carbocation is adjacent to a CH group, so it also has -hydrogens.
Thus, A, C, and D have the same number of hyperconjugative structures, while B does not.
Therefore, the correct option is A.
Counting $$\beta$$-Hydrogens
Given: Hyperconjugation count is required for the four cyclic cations.
Find: The set of cations having equal hyperconjugation.
Use the rule:
Applying this:
So the equal counts occur for A, C and D.
Hence, the correct option is A.
Counting the total number of hydrogens in the whole structure instead of only the -hydrogens. This is wrong because hyperconjugation in carbocations depends only on hydrogens on carbons adjacent to the positively charged carbon. Count only the adjacent-carbon hydrogens.
Treating a CH group and a CH group as contributing equally. This is wrong because CH provides -hydrogens, while CH provides . Distinguish the adjacent group correctly before comparing structures.
Comparing ring size or substitution pattern without locating the carbocation center first. This is wrong because the hyperconjugation count is a local effect near the positive charge. First mark the carbocation carbon, then inspect its neighboring carbons.
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