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In the preamble of the Indian Constitution, `X` refers to the day when the Constitution was adopted by the Constituent Assembly. This happened on the twenty-sixth day of November, 1949. Thus, option-2 is the correct answer.
To discuss the other options:
Option-1, the `twenty-sixth day of January, 1950`, is the day when the Constitution of India came into full effect and India became a republic, but it is not the day when the Constitution was adopted.
Option-3, the `twenty-sixth day of January, 1949` is incorrect because the constitution was neither adopted nor effected on this date.
Option-4, `None of the above` is not correct as `X` definitely stands for a specific date which the Constituent Assembly adopted the constitution, which is November 26, 1949.