Reasons why the Permanent Settlement was rarely extended to any region beyond Bengal:

Introduction:
The Permanent Settlement was a revenue system implemented by the British East India Company in Bengal in 1793. It aimed to fix the revenue demand from the landholders, known as zamindars, in perpetuity. However, this system was not extended to other regions in India due to several reasons.

1. Colonial state's desire to claim a share of enhanced income:
The primary reason why the Permanent Settlement was not extended to other regions was that the colonial state wanted to claim its share on the enhanced income of zamindars. Under this settlement, the revenue demand from the landholders was fixed, and any increase in income due to agricultural improvements or rise in land value would go entirely to the zamindars. The colonial state, realizing the potential of increasing revenue from the agrarian sector, did not want to forgo the opportunity to benefit from the economic progress.

2. Lack of loyalty to the company:
Another reason for not extending the Permanent Settlement was the colonial state's concern about creating a class of zamindars who would be loyal only to the company. The system of Permanent Settlement granted the zamindars hereditary rights over the land, giving them a significant amount of power and influence. If this system was extended to other regions, it could potentially create a powerful class of zamindars who might challenge the authority and control of the British East India Company. The company wanted to maintain its grip on power and feared losing control over the administration.

3. Peasant opposition to investment in agriculture:
Contrary to option (a), it is unlikely that peasants wanted to discourage investment in agriculture. Peasants were already burdened with heavy land taxes and were often exploited by the zamindars. The Permanent Settlement did not provide any relief to the peasants, and they continued to face high rents and arbitrary increases in revenue demand. Therefore, it is unlikely that they would have actively discouraged investment in agriculture.

4. Desire for revenue demand to be permanent:
The option (d) correctly states that the colonial state wanted the revenue demand to be permanent. By implementing the Permanent Settlement, the British East India Company aimed to establish a stable and fixed revenue system that would provide a consistent income stream. This would enable the company to plan its finances better and ensure a steady flow of revenue from the agrarian sector.

Conclusion:
In conclusion, the Permanent Settlement was rarely extended to regions beyond Bengal because the colonial state wanted to claim its share on the enhanced income of zamindars and did not want to create a class loyal only to the company. Additionally, the desire for a permanent revenue demand and the lack of peasant opposition to investment in agriculture also played a role in the limited extension of the Permanent Settlement.