In black pepper and beet, a part of the nucellus remains unused. What is this persistent nucellus called?

In most species,fruits develop from the process of fertilization. However,in some species,fruits develop without fertilization. This process is known as .......

Why is vivipary (germination of seeds while still attached to the parent plant) an undesirable trait for annual cereal crops?

Statement-$I$: Seeds generate new genetic combinations leading to variations.
Statement-$II$: Seeds are the product of sexual reproduction.

$A$: Fruit is a mature or ripened ovary,developed after fertilization.
$R$: If a fruit is formed without fertilization of the ovary,it is called a parthenocarpic fruit.

In angiosperms,which part remains attached after fertilization?