The correct answer is option-3, Laterite soil. Laterite soil is known for its poor fertility, making it the most infertile among the given options. Let`s examine the other options to understand why they are not the correct answer:

- Option-1: Black cotton soil is a fertile soil type found in regions with a high rainfall. It is suitable for agriculture and is known for its ability to retain moisture.

- Option-2: Alluvial soil is formed by the deposition of silt, sand, and clay by rivers. It is highly fertile and supports agriculture.

- Option-4: Peaty soil is formed by the accumulation of partially decomposed organic matter. It has high fertility and is suitable for soil-based gardening.

Although the provided answer is generally correct, it should be noted that the fertility of a soil type can vary depending on various factors such as climate, management practices, and nutrient content.