Assertion (A) Gulab Singh demarcated the boundaries of the princely state of Jammu and Kashmir. Reason (R) Gulab Singh signed the Treaty of Amritsar and acquired the rights of hilly regions between Indus and Ravi.

The correct answer is: C. Both A and R are true and R is the correct explanation of A.

Gulab Singh was the founder of the princely state of Jammu and Kashmir. He signed the Treaty of Amritsar in 1846 with the British East India Company, in which he acquired the rights of the hilly regions between Indus and Ravi in exchange for a sum of Rs. 75 lakhs. This treaty demarcated the boundaries of the princely state of Jammu and Kashmir.

Therefore, both assertion (A) and reason (R) are true. Moreover, reason (R) is the correct explanation of assertion (A). This is because the Treaty of Amritsar was the instrument that demarcated the boundaries of the princely state of Jammu and Kashmir.

Here is a brief explanation of each option:

• Option A: A is true but R is false. This is incorrect because reason (R) is true. The Treaty of Amritsar did indeed demarcate the boundaries of the princely state of Jammu and Kashmir.
• Option B: A is false but R is true. This is incorrect because assertion (A) is true. Gulab Singh did indeed sign the Treaty of Amritsar and acquire the rights of the hilly regions between Indus and Ravi.
• Option C: Both A and R are true and R is the correct explanation of A. This is the correct answer because both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
• Option D: Both A and R are true but R is not the correct explanation of A. This is incorrect because reason (R) is the correct explanation of assertion (A).