Explanation:

Serfoji II Bhonsle was the last ruler of the Bhonsle dynasty of the Maratha principality of Tanjore to exercise absolute sovereignty over his dominions. Serfoji’s modernising projects included the establishment of a printing press (the first press for Marathi and Sanskrit) and enrichment of the Saraswati Mahal Library.

• The Saraswati Mahal library, built by the Nayak rulers and enriched by Serfoji II contains a record of the day-to-day proceedings of the Maratha court - as Modi documents, French-Maratha correspondence of the 18th century. Modi was the script used to write the Marathi language. Hence, statement 1 is incorrect.
• Serfoji’s most striking initiative was the founding and management of free elementary and secondary schools for orphans and the poor in Thanjavur city and other adjacent places. Serfoji II established Dhanvantari Mahal, a research institution that produced herbal medicine for humans and animals.
• Hence, statement 2 is correct. Serfoji II was a patron of traditional Indian arts like dance and music.
• He authored Kumarasambhava Champu, Devendra Kuravanji, and Mudra rakshaschaya. He introduced western musical instruments like clarinet, and violin in Carnatic music.
• Hence, statement 3 is correct. He is also credited with popularising the unique Thanjavur style of painting.