Why C? And why not the others?

Correct answer: C. Canberra

Canberra is a capital built out of a rivalry. When Australia federated in 1901, Sydney and Melbourne both wanted the honour so badly that the constitution brokered a truce: the capital had to sit in New South Wales but at least 100 miles from Sydney. A sheep-station district was chosen, an international design competition was won by American architect Walter Burley Griffin, and Parliament finally moved in come 1927. Sydney tempts as the biggest and most famous city, Melbourne actually served as the interim seat of government until 1927, and Brisbane is only the state capital of Queensland - none of them is the national capital.

Source: Britannica: Canberra; Australian Capital Territory (constitution section 125, 1927 transfer)