Which of the following cell components shares its function of containing genetic material with the nucleus?

The choice of chromosomes as the correct answer is accurate because chromosomes are structures within the cell that consist of DNA, which carries the genetic information. In eukaryotic cells, chromosomes are found within the nucleus, which serves to house and protect this genetic material. The nucleus acts as the control center of the cell, regulating gene expression and cell division through the use of genetic information stored in the chromosomes.

While the nucleolus is involved in the production of ribosomes and is located within the nucleus, it does not contain genetic material itself. Ribosomes are essential for protein synthesis but do not store or contain genetic material. The plasma membrane serves as a barrier to protect the cell and regulates the entry and exit of substances but is not involved in the storage or protection of genetic material. Thus, chromosomes are the direct carriers of genetic information, making them the appropriate choice in relation to the nucleus.