Why B? And why not the others?

Correct answer: B. Nauru

Nauru's government offices sit in the Yaren district, which functions as the de facto seat of government, housing the parliament and administrative buildings, but Yaren has never been granted any special legal status above Nauru's other thirteen districts, so the country has never designated an official capital by law - a rare case among the world's sovereign states. Tuvalu's seat of government is Funafuti, which is that country's officially named capital atoll, not an omission of one. Kiribati's capital is South Tarawa, again formally designated as such. Palau's capital, Ngerulmud, is likewise an officially designated seat of government, moved there from Koror in 2006, so all three of these are simply countries whose capitals are small or unfamiliar, not ones lacking a designated capital altogether.

Source: Britannica: Naoero (Nauru), government and capital section; corroborated by CIA World Factbook, Nauru entry