Which of the following statements about the number of geometrical isomers is/are correct?

A $CH X_{3} - CH = CH - CH = CH - CH X_{2} CH X_{3}$ (hepta-2,4-diene) has $3$ geometrical isomers.
B $CH X_{3} - CH = CH - CH = CH - CH = CH - CH X_{3}$ (octa-2,4,6-triene) has $6$ geometrical isomers.
C $CH X_{3} - CH = CH - CH = CH - CH X_{3}$ (hexa-2,4-diene) has $3$ geometrical isomers.
D $CH X_{3} - CH = C (CH X_{3}) - CH = CH - CH X_{3}$ (3-methylhexa-2,4-diene) has $3$ geometrical isomers.

Answer: B, C

Unsymmetrical polyenes with

n

stereogenic

C = C

give

2^{n}

isomers. Symmetrical ones give

2^{n - 1} + 2^{(n - 1) /2}

for odd

n

and

2^{n - 1} + 2^{n /2 - 1}

for even

n

: hexa-2,4-diene (

n = 2

) gives

2 + 1 = 3

, and octa-2,4,6-triene (

n = 3

) gives

4 + 2 = 6

. Hepta-2,4-diene is unsymmetrical:

2^{2} = 4

, not

3

. 3-Methylhexa-2,4-diene has two stereogenic bonds and no symmetry:

4

, not

3

. Correct: A and C.