The correct answer is Option 1: Aurobindo Ghosh.

Aurobindo Ghosh, also known as Sri Aurobindo, was an influential figure in the Indian independence movement and a key leader of the extremist faction within the Indian National Congress during the early 20th century. He was a prominent nationalist, philosopher, poet, and yogi.

Aurobindo Ghosh criticized the moderate politics of the Indian National Congress in a series of articles entitled "New Lamps for Old." These articles were published in the Bengali newspaper "Bande Mataram," which Aurobindo himself edited.

In these articles, Aurobindo provided a systematic critique of the moderate approach adopted by the Indian National Congress, advocating for a more radical and assertive stance in the fight for Indian independence. He argued that the moderate leaders of the Congress, who believed in peaceful negotiations and constitutional reforms, were too passive and cautious in their approach.

Aurobindo Ghosh called for a more aggressive and militant strategy to achieve independence from British rule. He emphasized the need for a complete rejection of British domination and advocated for the use of revolutionary methods, including boycotts, strikes, and even armed resistance if necessary. Aurobindo`s writings greatly influenced the revolutionary activities and ideologies of the time.

It`s important to note that the other options mentioned in the question are not associated with the critique of the moderate politics of the Indian National Congress in the specific context mentioned. R.C. Dutt was an economist and a leader of the moderate faction within the Congress. Syed Ahmad Khan was a 19th-century Muslim reformer and educator, while Viraraghavachari was an Indian lawyer and politician associated with the Justice Party.