Tricarpellary, syncarpous gynoecium is found in these flowers

The correct option is Liliaceae.

To understand why this is correct, let us break down the terms describing the gynoecium (the female reproductive organ of a flower) in the question:
1. Tricarpellary: This means the gynoecium is composed of three carpels (the individual units of the pistil).
2. Syncarpous: This indicates that these three carpels are fused or joined together, rather than being free (apocarpous).

Let us analyze the characteristic gynoecium structure of the botanical families listed in the options:

• Liliaceae (Lily family): Members of this family typically possess a gynoecium that is tricarpellary (three carpels), syncarpous (fused carpels), and has a superior ovary with axile placentation. Examples include onion, tulip, and lily. Therefore, a tricarpellary, syncarpous gynoecium is a defining feature of the Liliaceae family.
• Poaceae (Grass family): The gynoecium is usually monocarpellary (or appearing monocarpellary due to reduction of two carpels out of three) with a single ovule and basal placentation.
• Solanaceae (Potato family): The gynoecium is typically bicarpellary (two carpels) and syncarpous, with a superior ovary and axile placentation.
• Fabaceae (Legume family): The gynoecium is monocarpellary (single carpel) with a superior, unilocular ovary and marginal placentation.

Consequently, a tricarpellary, syncarpous gynoecium is characteristically found in the flowers of the Liliaceae family.