To solve this problem, we need to identify which plant family has a tricarpellary, syncarpous gynoecium. Let's analyze each option:$\newline \bullet$Liliaceae:$\newline$ - The Liliaceae family is known for having a tricarpellary, syncarpous gynoecium.$\newline$ - This means the gynoecium consists of three fused carpels.$\newline$ - Examples include lilies, which are characteristic members of this family.$\newline \bullet$Solanaceae:$\newline$ - The Solanaceae family typically has a bicarpellary, syncarpous gynoecium.$\newline$ - This means the gynoecium consists of two fused carpels.$\newline$ - Examples include tomatoes and potatoes.$\newline \bullet$Fabaceae:$\newline$ - The Fabaceae family usually has a monocarpellary gynoecium.$\newline$ - This means the gynoecium consists of a single carpel.$\newline$ - Examples include beans and peas.$\newline \bullet$Poaceae:$\newline$ - The Poaceae family generally has a monocarpellary gynoecium.$\newline$ - This means the gynoecium consists of a single carpel.$\newline$ - Examples include grasses like wheat and rice.$\newline$Based on this analysis, the correct answer is Option 1: Liliaceae, as it has a tricarpellary, syncarpous gynoecium.