The correct answer is option 1, which states that only statement 1 is correct.

Option 1 states that the Kumaramatyas were the most important officers, appointed directly by the King in the home provinces. This statement is correct. The Kumaramatyas were high-ranking officials responsible for various administrative and judicial functions in the Gupta dynasty. They were appointed directly by the King and played a crucial role in governing the kingdom.

Option 2, which states that village headmen lost importance and land transactions began to be effected without their consent, is incorrect. During the Gupta dynasty, village headmen continued to hold significance and played a vital role in local administration. They were responsible for collecting taxes, maintaining law and order, and representing the interests of the villagers. Land transactions and other important decisions within the villages required their consent.

In summary, while statement 1 is correct, statement 2 is incorrect. Therefore, the correct answer is option 1.