Introduction:
The synthesis of RNA and DNA in vitro refers to the process of creating these nucleic acids outside of a living organism, typically in a laboratory setting. This technique has played a crucial role in advancing our understanding of molecular biology and genetics. The question asks about the scientists who first carried out this groundbreaking work.

Explanation:
The correct answer to the question is option 'C' - Ochoa and Kornberg. Here is a detailed explanation of their contributions:

1. Severo Ochoa:
- Severo Ochoa was a Spanish-American biochemist who made significant contributions to the field of molecular biology.
- In the 1950s, Ochoa began studying the process of RNA synthesis, specifically the enzymatic reactions involved.
- In 1955, Ochoa successfully isolated and characterized the enzyme polynucleotide phosphorylase (PNPase) from bacteria, which was capable of synthesizing RNA in vitro.
- This discovery opened up new possibilities for studying the structure and function of RNA molecules.

2. Arthur Kornberg:
- Arthur Kornberg was an American biochemist who made significant contributions to the field of DNA replication.
- In the late 1950s, Kornberg focused on the enzymatic reactions involved in DNA synthesis.
- In 1956, Kornberg successfully isolated and characterized the enzyme DNA polymerase I from bacteria, which was capable of synthesizing DNA in vitro.
- This groundbreaking work earned Kornberg the Nobel Prize in Physiology or Medicine in 1959.

3. Collaboration:
- Ochoa and Kornberg collaborated on several occasions, combining their expertise in RNA and DNA synthesis.
- In 1959, they jointly published a paper titled "Enzymic Synthesis of DNA," which described the enzymatic synthesis of DNA in vitro using DNA polymerase.
- This paper demonstrated the ability to replicate DNA outside of living cells, marking a significant breakthrough in molecular biology.

Conclusion:
In conclusion, the in vitro synthesis of RNA and DNA was first carried out by Ochoa and Kornberg. Their groundbreaking work in isolating and characterizing the enzymes responsible for RNA and DNA synthesis paved the way for further advancements in the field of molecular biology.