The correct answer is option 1: 1 only.

Statement 1 states that under Akbar, the system of Zabt was established over a large area from Punjab to Awadh. The system of Zabt was a revenue collection system introduced by Akbar which involved fixing the revenue demand in cash in accordance with the evaluation of the potential of the land. It was implemented effectively in many regions under Akbar`s rule, including Punjab and Awadh.

Statement 2 states that in the seventeenth century North India, the system of Zabt lost much ground to the system of Kankut. However, this statement is incorrect. The system of Zabt continued to be an important revenue collection system even in the seventeenth century, and there is no evidence to suggest that it lost ground to the system of Kankut.

Therefore, only statement 1 is correct, and the correct answer is option 1.