The nucleus is not important as the site of:
(a) DNA synthesis
(b) RNA synthesis
(c) Synthesis of ribosomal subunits
(d) Protein synthesis

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Hint: The nucleus controls and regulates the activities of the cell and also carries the genes, which are structures containing the hereditary information. Protein synthesis essentially takes place in Ribosomes in the cytoplasm.

Complete answer: Nucleus, is, a specialized important structure occurring in most cells (except in bacteria and BGA).

It is separated from the rest of the cell by a double layer, known as the nuclear membrane. The nucleus basically controls and regulates the activities of the cell (e.g., growth and metabolism) and carries the genes, structures that contain the hereditary information.
It primarily serves as the information centre of the cell.

Information in DNA is transcribed into a range of messenger ribonucleic acid (mRNA) molecules, each of them encodes the information for one protein.
The mRNA molecules are then transported through the nuclear envelope into the cytoplasm, further where they are translated, hence serving as templates for the synthesis of specific proteins through the processes transcription & translation.
Without a nucleus, the cell will not know how to function and there would be no regulation of cell division.

Additional information: Even, protein synthesis would either cease or incorrect proteins would be formed. After the transcription of DNA to mRNA is complete, translation begins.
Protein synthesis takes place in the ribosomes (present in the cytoplasm), and hence, nucleus is not an important site for the synthesis of proteins.
So, the correct answer is ‘Protein synthesis’.
Note: A cell normally contains only one nucleus. Although, in some cases the nucleus divides but the cytoplasm does not. This produces a multinucleate cell (syncytium) such as in the case of skeletal muscle fibers and even in fungal hyphae. Some cells—e.g., the human red blood cell—lose their nuclei upon maturation.