Final answer:
The rough endoplasmic reticulum does not contain DNA. The nucleus, chloroplast, and mitochondrion all contain DNA, as these organelles are directly involved in genetic material storage and energy production in eukaryotic cells.
Step-by-step explanation:
The organelle that does NOT contain DNA among the options provided is the rough endoplasmic reticulum. In eukaryotic cells, the nucleus is known to contain the bulk of the cell's genetic material in the form of DNA. The chloroplast, found in plant cells and some protists, contains its own DNA, which is evidence of its evolutionary origin from endosymbiotic cyanobacteria. The mitochondrion, an organelle present in most eukaryotic cells, also contains its own DNA, a remnant from its ancestry as a free-living bacterium that was engulfed by an ancestral eukaryotic cell. This mitochondrion is responsible for the production of ATP, the energy currency of the cell.