A) Texas v. Johnson (1989) INCORRECT This case dealt with the First Amendment right to freedom of speech, specifically whether flag burning constitutes protected symbolic speech. The Supreme Court ruled in favor of Johnson, stating that the government cannot prohibit expression merely because it is offensive. This decision reinforced individual liberties, not federal authority over states, and does not relate to the establishment of federal institutions.
B) Plessy v. Ferguson (1896) INCORRECT This case upheld the constitutionality of racial segregation under the 'separate but equal' doctrine. It involved state laws requiring segregated facilities, and the Court ruled that such laws did not violate the Fourteenth Amendment's Equal Protection Clause. This decision actually reinforced state authority to enforce segregation, not federal authority over states, and it was later overturned by Brown v. Board of Education.
C) McCulloch v. Maryland (1819) CORRECT This case is the definitive answer because it directly addressed the federal government's power to establish a national bank and the inability of states to tax or interfere with federal institutions. The Supreme Court's ruling established the doctrines of implied powers and federal supremacy, ensuring that the federal government could operate without state obstruction. This reinforced the authority of the national government and is a key precedent in constitutional law.
D) Brown v. Board of Education of Topeka (1954) INCORRECT This landmark case declared state laws establishing separate public schools for black and white students to be unconstitutional, violating the Equal Protection Clause. While it reinforced federal authority in enforcing civil rights, it did not concern the establishment of a federal institution. Instead, it struck down state segregation laws, and its focus was on racial equality in education, not on the balance of power regarding federal institutions.