Propadiene (allene), shown, is achiral. In an allene the two terminal $\mathrm{CH}{}_2$ planes are perpendicular to each other. Which of the cumulated polyenes shown as options is chiral?

In an allene $\mathrm{R}{}_2\mathrm{C}=\mathrm{C}=\mathrm{CR}{}_2$ the substituents on the two ends lie in perpendicular planes, so the molecule is chiral when each terminal carbon carries two different groups. Structure P, penta-2,3-diene $\mathrm{CH}{}_3\mathrm{CH}=\mathrm{C}=\mathrm{CHCH}{}_3$, has $\mathrm{H}$ and $\mathrm{CH}{}_3$ on each end and no plane of symmetry: chiral. Q (3-methylbuta-1,2-diene) and S (2-methylpenta-2,3-diene) each have one end bearing two identical groups, so the plane of that end is a mirror plane. R, hexa-2,3,4-triene, has an even number of cumulated double bonds, so the two ends lie in the same plane and the molecule shows cis/trans isomerism but is achiral.