Number of cyclic isomers of C4H6 I faced a question 


  How many cyclic isomers are possible for $\ce{C4H6}$?


I and my friend found the following four.


But the answer key says there are 5. So what's the other one?
You can answer such questions using D.U. (Degree of unsaturation)

The formula is $\mathrm{C + 1 - }\frac{H + X - N}{2}$

C = Carbon.
H = Hydrogen.
X = Halogen.
N = Nitrogen.


If you get D.U. to be one, then in the structure there could be:


1 double bond.
1 ring.


Let's take an example of $\ce{C4H8}$ which has D.U. equal to one.


It can have three structures of 1 double bond:





It can have two structures of 1 ring:




Now for D.U. equal to two, the possibilities are:


2 double bond.
2 ring.
1 double bond and 1 ring.
1 triple bond.


Let's take your example of $\ce{C4H6}$ which has D.U. equal to two:


It can have two structures of 2 double bond:





It can have one structure of 2 ring:





It can have four structures of 1 double bond + 1 ring:





It can have two structures of 1 triple bond:




So, the answer is 5 cyclic isomers as you can see above.