Analysis of Assertion and Reason:

Kautilya's Emphasis on Strong Ruler (Assertion A)

Assertion (A) states that Kautilya emphasizes the need for a strong ruler. Kautilya, in his seminal work 'Arthashastra', details the administrative and political structure of an ideal state. His theories extensively cover the duties, responsibilities, and powers of the king, advocating for a robust and authoritative leadership to ensure the state's welfare and stability. Therefore, Assertion (A) is factually correct.

Kautilya's Awareness of Anarchy (Reason R)

Reason (R) suggests that Kautilya was acutely aware of the dangers of anarchy and the necessity of establishing social order. Kautilya identified 'Matsyanyaya' (the law of the fishes, where the bigger fish eats the smaller ones) as the state of nature without a strong government. He believed that only a strong ruler and an organized state could prevent this chaos and ensure justice and order. Thus, Reason (R) is also factually correct.

R is the Correct Explanation of A

The reason provided in (R) directly supports and explains the assertion in (A). Kautilya's advocacy for a strong ruler stems precisely from his deep understanding that such leadership is essential to combat anarchy ('Matsyanyaya') and establish the necessary order for society to function and prosper. The need for order (Reason R) is the fundamental justification for the requirement of a strong ruler (Assertion A).

Conclusion

Since both Assertion (A) and Reason (R) are true, and Reason (R) provides the correct explanation for Assertion (A), the correct option is:

Option 1: Both (A) and (R) are true and (R) is the correct explanation of (A).