Local self-government can be best explained as an exercise in

The correct answer is B) Democratic decentralisation. Local self-government means elected bodies at the village, block, district or urban level manage local affairs. Power is passed down from the State to these bodies, and they remain accountable to the people who elect them. That combination of devolution and elected representation is what democratic decentralisation means.

Why the others fail:

• Federalism is a division of power between the Union and the States, laid down by the Constitution. Local bodies are not federal units. The States create them under Part IX and Part IXA, following the 73rd and 74th Amendments (1992).
• Administrative delegation transfers work to officials within the same hierarchy. They stay answerable upward to superiors, not to voters.
• Direct democracy means citizens decide issues themselves, through referendums or initiatives. Local government is representative, though Gram Sabhas add a participatory layer.

Core concept: the 73rd and 74th Amendments created the three-tier Panchayati Raj and the municipal structure, along with State Election Commissions, State Finance Commissions and the Eleventh and Twelfth Schedules. For Mains GS-II, expect questions on why devolution of funds, functions and functionaries (the 3Fs) remains uneven across States.

Trap: Aspirants pick federalism because local government sits within a multi-tier system. Federalism concerns the Union-State division, while local government is a third tier, which is decentralisation.