Explanation: To understand the context of the question, it is essential to delve into the historical timeline and the interactions between various rulers and religious figures in West Bengal and neighboring regions.
**Sultan Allauddin Hussain and Chaitanya:**
Sultan Allauddin Hussain Shah ruled Bengal from 1493 to 1519, and later from 1519 to 1532. Chaitanya Mahaprabhu, a prominent Vaishnavite saint, lived from 1486 to 1533. Their lifetimes overlapped, making them contemporaries. Chaitanya's influence extended beyond Bengal, and he is known for his contributions to Vaishnavism and the Bhakti movement. The first statement is correct as it accurately reflects the contemporaneous nature of these two figures.
**Gajapati Rulers and Puri Temples:**
The Gajapati rulers of Orissa, who were successors to the Eastern Ganga dynasty, are indeed known for their contributions to the construction and maintenance of the famous Puri Jagannath Temple. The temple complex is one of the four major pilgrimage sites in Hinduism, known as the Char Dham. However, the Gajapati rulers were not contemporaneous with the Vijayanagara Empire, which emerged in the 14th century and flourished until the 16th century. The second statement is partially correct but incomplete.
**Ganga Rulers and Vijayanagara State:**
The Ganga rulers of Orissa, who ruled from the 11th to the 14th century, were not in conflict with the Vijayanagara state. The Vijayanagara Empire was established in the 14th century, long after the Ganga rulers had ceased to rule. The Vijayanagara Empire was primarily in conflict with the Bahmani Sultanate and other Deccan Sultanates. The third statement is incorrect.
In summary, the first statement is correct as it accurately reflects the contemporaneous nature of Sultan Allauddin Hussain and Chaitanya. The second statement, while partially correct, does not address the conflict with the Vijayanagara state, which is incorrect. The third statement is entirely incorrect. Therefore, the correct answer is Option A: 1 only.