Meiosis occurs in two stages - meiosis I and meiosis II. The meiosis I is characterised by pairing of homologous chromosomes, crossing over and separation of homologous chromosomes. The centromere remains intact during meiosis I and homologous chromosomes separate. Thus, the number of chromosomes in progeny nuclei is reduced to one half. In meiosis II, just as mitosis, centromere separate and, hence, the number of chromosomes in the progeny remains same.

Meiosis I is the first division in the process of meiosis, which is a type of cell division that occurs in sexually reproducing organisms. During meiosis I, the number of chromosomes is reduced by half, resulting in the production of haploid cells (gametes) from diploid cells.

During meiosis I, the centromere is the region of a chromosome where the two sister chromatids are held together. The centromere plays a crucial role in ensuring the proper separation of chromosomes during cell division.

The correct answer to the given question is option 'D' - No division. This means that the centromere does not undergo division during meiosis I. Let's understand why this is the correct answer:

- Meiosis I consists of several stages: prophase I, metaphase I, anaphase I, and telophase I. In prophase I, the chromatin condenses to form visible chromosomes, and homologous chromosomes pair up and undergo a process called synapsis. During synapsis, the homologous chromosomes align closely and form structures called bivalents or tetrads.
- In metaphase I, the bivalents align along the equatorial plane (metaphase plate) of the cell. The centromeres of homologous chromosomes attach to spindle fibers from opposite poles of the cell.
- In anaphase I, the homologous chromosomes separate and move towards opposite poles of the cell. This separation is called disjunction. However, the sister chromatids of each chromosome remain attached at their centromeres and do not separate during anaphase I.
- Finally, in telophase I, the chromosomes reach the opposite poles of the cell, and the nuclear envelope reforms around each set of chromosomes. The cell then undergoes cytokinesis, resulting in the formation of two daughter cells.

Therefore, it is clear that the centromere does not undergo division during meiosis I. It is only in meiosis II, the second division of meiosis, that the sister chromatids separate and the centromeres divide.

Overall, the correct answer is option 'D' - No division, as the centromere remains intact during meiosis I.