**Answer:**

The correct answer is option B - On 1st October 1953.

**Explanation:**

The state of Andhra Pradesh came into existence on 1st October 1953, as a result of the States Reorganization Act of 1956. However, it is important to note that Andhra Pradesh was initially formed on 1st November 1953 as a separate state, before merging with Telangana to form Andhra Pradesh on 1st November 1956.

Here is a detailed explanation of the events leading to the formation of Andhra Pradesh:

**1. The demand for Andhra State:**

The demand for a separate Andhra state emerged in the 1920s and gained momentum in the 1950s. The Andhra Mahasabha, a political organization, played a significant role in advocating for the creation of a separate Andhra state.

**2. The States Reorganization Commission (SRC):**

In 1953, the Government of India constituted the States Reorganization Commission (SRC) to investigate and recommend the reorganization of states on a linguistic basis. The SRC was tasked with creating states that would have linguistic and cultural homogeneity.

**3. Formation of Andhra State:**

Based on the recommendations of the SRC, the government decided to create the Andhra State by separating the Telugu-speaking areas from the Madras State. On 1st October 1953, the Andhra State was formed with Kurnool as its capital.

**4. Merger with Telangana:**

The demand for a separate Telangana state, consisting of the Telugu-speaking areas of the princely state of Hyderabad, also gained momentum during this period. After several years of agitation and protests, the government agreed to the formation of a separate Telangana state.

**5. Formation of Andhra Pradesh:**

To address the demands for both Andhra and Telangana, the government passed the States Reorganization Act in 1956. As per this act, the Andhra State and Telangana were merged to form a single state called Andhra Pradesh on 1st November 1956. The new state had its capital in Hyderabad.

In conclusion, the new state of Andhra Pradesh came into being on 1st October 1953, when the Andhra State was formed. However, it merged with Telangana to form Andhra Pradesh on 1st November 1956.