Which of the following articles of the Indian constitution made the provision for use of English. Alongside Hindi. For official purposes, for fifteen years?

The correct option is Article 343.

Let us understand the provision step-by-step:
1. Official Language of the Union: Article 343(1) of the Indian Constitution specifies that the official language of the Union shall be Hindi in Devanagari script.
2. Provision for English: Article 343(2) states that notwithstanding anything in clause (1), for a period of fifteen years from the commencement of the Constitution (i.e., from January 26, 1950, to January 26, 1965), the English language shall continue to be used for all the official purposes of the Union for which it was being used immediately before such commencement.
3. Extension of English: Article 343(3) gave Parliament the power to provide by law for the use of the English language even after the period of fifteen years, which eventually led to the passage of the Official Languages Act, 1963.

Therefore, Article 343 is the specific constitutional provision that allowed the use of English alongside Hindi for official purposes for the initial fifteen-year period.