What caused the increase in the population of darker, melanistic form…

The correct answer is Option (2) → Natural selection favouring moths better camouflaged against darkened tree trunks

The peppered moth of England is the book’s example of natural selection. Before industrialisation, tree trunks were covered with pale lichens, so white-winged moths were hidden and dark moths were picked out by birds. Later, industrial smoke and soot darkened the trunks. Now the dark (melanised) moths were hidden and the white ones were eaten. The moths that matched the background survived and became more common.

Option (1) A decrease in the population of predators — Incorrect. The predators were still there. In fact it was predation that removed the white moths from the dark trunks.

Option (2) Natural selection favouring moths better camouflaged against darkened tree trunks — Correct. The dark moths were camouflaged against the darkened tree trunks, so birds missed them. Natural selection favoured them, and their numbers rose.

Option (3) An increase in the population of white-winged moths — Incorrect. In industrial areas the white-winged moths did not survive, because birds could see them on the dark trunks. Their number fell, not rose.

Option (4) Genetic mutation unrelated to environmental changes — Incorrect. The change was linked to the environment: it followed the darkening of the trunks. In rural areas without industry, melanic moths stayed few.

NCERT Extract:
What Are the Evidences for Evolution? – “The explanation put forth for this observation was that ‘predators will spot a moth against a contrasting background’. During postindustrialisation period, the tree trunks became dark due to industrial smoke and soots. Under this condition the white-winged moth did not survive due to predators, dark-winged or melanised moth survived. … Hence, moths that were able to camouflage themselves, i.e., hide in the background, survived (Figure 6.4).”