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The correct answer is option 4: 26 January 1957.
Option 1: 15 August 1946 is not the correct answer. This date is significant as it marks the independence of India from British rule, but it is not specifically related to the Constitution of Jammu and Kashmir.
Option 2: 15 August 1947 is also not the correct answer. This date marks the independence of both India and Pakistan, but again, it is not directly related to the Constitution of Jammu and Kashmir.
Option 3: 26 January 1950 is not the correct answer either. This date is important as it is when the Constitution of India came into effect, but it is not the same as the Constitution of Jammu and Kashmir.
Therefore, the correct answer is option 4: 26 January 1957. This date signifies when the Constitution of Jammu and Kashmir was implemented and came into force.