Nizam-ul-Mulk Tusi served as the powerful Wazir to the Seljuq Sultans Alp Arslan and Malik Shah I. The provided option 'Nizam Shah' is historically inaccurate as he served the Seljuq dynasty, not a ruler by that name. This reflects a potential error in the source material regarding the historical figure's title.

In Kautilya's Saptanga theory, the state is composed of seven limbs (angas). Amatya represents the administrative and bureaucratic element. It encompasses the high-ranking officials, ministers, and executive officers who are essential for the day-to-day governance and the implementation of the king's policies. Without a competent administrative body, the state cannot function effectively, making Amatya a crucial pillar of the sovereign state structure.

Nizam al-Mulk Tusi, in his seminal work 'Siyasat Nama' (Book of Government), articulated the view that the ruler is divinely chosen to maintain order and justice. He emphasized the necessity of a strong, centralized administration to ensure the stability of the state and the welfare of the subjects, reflecting the administrative traditions of the Seljuk Empire.

Nizam-ul-Mulk Tusi was a prominent Persian scholar and vizier of the Seljuk Empire. He is celebrated for his profound political wisdom, most notably documented in his work 'Siyasat Nama' (Book of Government). His writings provided a comprehensive framework for statecraft, administration, and the ethical conduct of rulers, which influenced Islamic political thought for centuries.

Prabhusakti refers to the financial power or the strength of the treasury of a state. In ancient political thought, particularly in the context of statecraft, a strong treasury was considered essential for maintaining an army, supporting the administration, and ensuring the stability of the kingdom. It is one of the key components of a ruler's power, as financial resources enable the state to project authority and provide for its citizens.

The Siyasat Namah, or 'Book of Government,' was written by the Persian vizier Nizam al-Mulk. It serves as a comprehensive guide for rulers on administration, justice, and the maintenance of the state. The work is structured into 50 distinct chapters that cover various aspects of governance, ethics, and the duties of a monarch in the Seljuk Empire.

In the Arthashastra, Kautilya uses an organic theory of the state. The matching provided in option B corresponds to his specific analogies: Amatya (ministers) as the eyes, Suhrid (allies) as the ears, Durga (fort) as the arms, and Kosha (treasury) as the mouth. This organic view emphasizes that the state is a living entity where each part must function correctly for the health and survival of the whole body politic.

Abu Ali al-Hasan ibn Ali ibn Ishaq al-Tusi, known as Nizam al-Mulk, was born in the year 1017 or 1018 AD in the region of Tus, located in modern-day Iran. He rose to prominence as a scholar and a highly influential vizier under the Seljuk sultans Alp Arslan and Malik-Shah I, leaving a lasting legacy in administrative governance.

Nizam al-Mulk Tusi, the influential vizier of the Seljuk Empire, authored 'Siyasat Nama' (The Book of Government). This work is a classic of Persian political literature, providing comprehensive advice on statecraft, the administration of justice, the management of the military, and the moral duties of the ruler, reflecting the political realities of the 11th century.

'Dastur al-Wuzara' is a work on governance and the role of the vizier, attributed to Nizam al-Mulk Tusi. As a high-ranking official in the Seljuk Empire, Tusi wrote extensively on the responsibilities of ministers, the importance of bureaucratic efficiency, and the ethical conduct required for those serving the state, making this a foundational text in Islamic administrative history.