In which of the following cases did the Supreme court of India give a ruling that, 'in case of any conflict between the fundamental rights and the directive principles, the former would prevail'?

The correct answer is Champakam Dorairajan Case, 1951. In State of Madras v. Champakam Dorairajan, the Supreme Court struck down a Madras government order that reserved college seats by community. The State defended it as carrying out Article 46, a Directive Principle, but the Court held that the Directive Principles must conform to and run subsidiary to the chapter on Fundamental Rights, so in any conflict the Fundamental Rights prevail. The judgment also led directly to the 1st Amendment of 1951, which added Article 15(4) to permit special provisions for backward classes.

The other cases came later and went further. Golaknath (1967) held that Parliament cannot amend Fundamental Rights at all, even to implement Directive Principles. Kesavananda Bharati (1973) held that Parliament can amend any part of the Constitution but not its basic structure. Minerva Mills (1980) held that the balance between Fundamental Rights and Directive Principles is itself part of the basic structure. Read in order, the four cases show how the Court moved from "rights first" to "rights and directives in balance".