This structure tends to vanish always during meiosis and mitosis

The correct option/answer is Nucleolus and nuclear membrane.

During the cell division processes of both mitosis and meiosis, a cell undergoes a series of highly coordinated stages to ensure the proper segregation of genetic material. The first active stage of division is prophase (or prophase I in meiosis).

During prophase, several key structural changes occur to prepare the cell for chromosome alignment and separation:
1. The chromatin condenses into distinct chromosomes.
2. The nucleolus, which is the site of ribosome biogenesis, gradually disappears. This is because the transcription of ribosomal RNA ceases as the chromosomes condense.
3. The nuclear membrane (or nuclear envelope) breaks down into small vesicles. Disassembly of the nuclear membrane is crucial because it allows the spindle fibers, which originate from the centrosomes in the cytoplasm, to access and attach to the chromosomes at their kinetochores.

These structures remain absent through metaphase and anaphase, and they only begin to reform during telophase, which is the final stage of nuclear division. In contrast, other organelles like plastids and the plasma membrane do not vanish or disintegrate during cell division; the plasma membrane remains intact to define the boundary of the dividing cell, and organelles like plastids are partitioned between the daughter cells. Therefore, the nucleolus and nuclear membrane are the structures that consistently vanish during meiosis and mitosis.