Both option A and R are true statements. The war of independence in India did break out in 1857 soon after the departure of Lord Dalhousie from India. Lord Dalhousie`s annexationist policy, which involved annexing different regions of India into British territory, had caused great discontent among the Indian population. This discontent eventually led to the rebellion and the war of independence.

Option 1 states that both A and R are true, and R is the correct explanation of A. In this case, Lord Dalhousie`s annexationist policy can be seen as the cause of the war of independence, as the discontent it created among the Indian people played a significant role in sparking the rebellion.

It is important to note that the war of independence was not solely caused by Lord Dalhousie`s policies, but they certainly played a significant role in building the sentiment of discontent among the Indian population. Overall, option 1 correctly explains the relationship between A and R.

Therefore, option 1 is the correct answer.