A sun path diagram is nothing but a picture of where the sun sits in the sky through the day, drawn for a few key dates in the year. Its shape is a direct fingerprint of latitude, so this question really asks: which latitude gives which shape?
- New Delhi ($28^{\circ}$N): a subtropical location. The sun climbs high in summer and stays moderately low in winter, but day length does not vary as wildly as it does further from the equator, so its diagram shows a moderate spread between the seasonal paths.
- Singapore ($1^{\circ}$N): almost exactly on the equator. The sun tracks close to overhead through most of the year, so the seasonal paths bunch tightly together into a narrow, near-symmetric shape.
- Sydney ($34^{\circ}$S): a mid latitude, but in the southern hemisphere. The whole diagram flips compared to a northern mid latitude city, because the sun now arcs through the northern part of the sky as seen from there.
- Helsinki ($60^{\circ}$N): far to the north. Day length changes enormously between summer and winter here, so the summer and winter sun paths are pulled far apart from each other, giving the widest, most stretched-out diagram of the four.
Reading the diagrams with this logic: diagram 3 is the moderate subtropical shape (New Delhi), diagram 5 is the tight equatorial shape (Singapore), diagram 1 is the mirrored southern hemisphere shape (Sydney), and diagram 2 is the widely stretched high latitude shape (Helsinki).
Let's summarize:
- Sun path shape is set by latitude, not by anything else about the place.
- Equatorial cities give tight, near-symmetric diagrams; high latitude cities give widely stretched ones; southern hemisphere cities mirror their northern counterparts.
So P - 3, Q - 5, R - 1, S - 2, which is option (C).