If a cell contains a set of duplicated chromosomes, does it contain any more genetic information than the cell before the chromosomes were duplicated?

No.

Explanation:

When the set of chromosomes are duplicated, it means the chromosomes will be double the number.

However the genetic information will not change. It will remain the same.

Duplication of chromosomes is usually occurs among the interphase stage of mitosis where chromosomes will duplicate to ensure the formation of two identical daughter cells.

In these cells there will be no addition or variation in genetic information.