In an animal cell, the processes of transcription and translation occur in the nucleus and cytoplasm respectively.

Transcription and translation are two fundamental processes involved in gene expression and protein synthesis in cells. They occur in different cellular compartments and are tightly regulated to ensure proper protein production.

Transcription:
Transcription is the process by which genetic information encoded in DNA is copied into RNA. It takes place in the nucleus of eukaryotic cells, including animal cells. The steps involved in transcription are as follows:

1. Initiation: Transcription factors bind to specific DNA sequences called promoters, marking the start site for RNA synthesis. RNA polymerase, an enzyme responsible for synthesizing RNA, is recruited to the promoter region.

2. Elongation: RNA polymerase unwinds the DNA double helix and synthesizes an RNA molecule complementary to one of the DNA strands. The RNA molecule is known as the primary transcript or pre-mRNA.

3. Termination: Transcription ends when RNA polymerase reaches a termination sequence in the DNA. The pre-mRNA is then released.

Translation:
Translation is the process by which the genetic information encoded in RNA is used to synthesize proteins. It occurs in the cytoplasm of the cell and involves the following steps:

1. Initiation: The mRNA molecule carries the genetic code from the nucleus to the cytoplasm. In the cytoplasm, ribosomes bind to the mRNA at a specific start codon (usually AUG). Initiation factors help position the ribosome and the first aminoacyl-tRNA at the start codon.

2. Elongation: Aminoacyl-tRNAs, carrying specific amino acids, are brought to the ribosome and matched with the corresponding codons on the mRNA through base-pairing. The ribosome moves along the mRNA, synthesizing a polypeptide chain as it goes.

3. Termination: The process continues until a stop codon is encountered on the mRNA. At this point, a release factor binds to the ribosome, causing the polypeptide chain to be released. The ribosome and mRNA dissociate.

Conclusion:
In an animal cell, transcription occurs in the nucleus, where the DNA is located. The resulting pre-mRNA molecule is then transported out of the nucleus and into the cytoplasm. In the cytoplasm, the pre-mRNA is processed into mature mRNA, which serves as the template for translation. Translation takes place on ribosomes in the cytoplasm, where the mRNA is read to synthesize proteins. Therefore, the correct answer is option 'C' - transcription occurs in the nucleus, and translation occurs in the cytoplasm.