The cyclic cations having the same number of hyperconjugalion are :
A.

B. 

C. 

D. 

Choose the correct answer from the options given below :

Hyperconjugation in a carbocation is possible only with the hydrogens present on the carbon atoms directly bonded to the positively-charged carbon (α-carbons). Each such α-hydrogen can be displaced into the empty $$p$$-orbital of the cation to give one hyperconjugative (no-bond resonance) structure.
Therefore,

Number of hyperconjugative structures $$=\,$$ total number of α-hydrogens

We must inspect each of the four cyclic carbocations, count their α-hydrogens and then compare.

The positively-charged carbon is bonded to two equivalent CH3 groups (each supplies three hydrogens) and one carbon of the ring that bears no hydrogens. Hence
total α-hydrogens in A $$= 3+3 = 6$$

The cationic centre here is bonded to one CH3 group (three hydrogens) and two ring carbons that carry no hydrogens. Hence
total α-hydrogens in B $$= 3$$

This structure is identical to A in the sense that the cationic carbon is again attached to two CH3 groups and one ring carbon without hydrogens. Therefore
total α-hydrogens in C $$= 6$$

The cationic centre is attached to one CH2 group (two hydrogens) and two ring carbons devoid of hydrogens. Thus
total α-hydrogens in D $$= 2$$

Comparing the counts, only A and C possess the same number of α-hydrogens (six each), i.e. the same number of hyperconjugative structures.

Hence the cyclic cations that have an equal extent of hyperconjugation are A and C.

Option C which is: A and C Only