In which case will Federal law prohibit a state from imposing an income tax on net income?

Federal law prohibits a state from imposing an income tax on net income in situations where the business's activities do not constitute sufficient nexus within the state. The case where orders are taken within the state and shipped from outside illustrates a lack of enough physical presence. According to U.S. Supreme Court rulings, specifically Quill Corp. v. North Dakota, states cannot tax businesses whose only connection is limited to taking orders and shipping goods from outside their borders. This aligns with the principle of "nexus," which requires a substantial physical presence for a state to impose an income tax.

Having a retail outlet or corporate headquarters in the state indicates a physical presence, which generally allows for state taxation of income. Similarly, if orders are taken and accepted within the state, this establishes a level of business operation that would also support a state's authority to impose income tax. Thus, the correct identification of circumstances under which federal law prohibits state taxation focuses on the absence of sufficient nexus, as illustrated in the scenario where orders are taken in the state but fulfilled from outside.