Explanation:

Both statements 1&2 are incorrect.

Government of India is implementing Centrally Sponsored Scheme of National AYUSH Mission (NAM) through States/UTs for development and promotion of AYUSH system of medicine including Homoeopathy. Hence statement 1st is incorrect.

• Under NAM, Grant-in-aid is being provided to State/UT Governments for development and promotion of Ayurveda, Yoga & Naturopathy, Unani, Siddha and Homoeopathy (AYUSH) as per their proposed State Annual Action Plans (SAAPs). 
• Specific resource pool with respect to NAM for each State/UT Government is allocated and communicated by the Central Government. 
• Accordingly, the State/UT Governments submit their State Annual Action Plans (SAAPs) to the Ministry as per their felt need in accordance with NAM guidelines. 
• Since NAM is a Centrally Sponsored Scheme and implementation of the programme comes under the purview of respective States/UT Government, no specific targets have been fixed by Government of India in the States/UTs. Hence statement 2nd is incorrect.
• As Public Health is a State subject, setting up of AYUSH Hospitals and Dispensaries comes under the purview of respective State/UT Governments. Hence statement 3rd is correct.
• However, under Centrally Sponsored Scheme of National AYUSH Mission (NAM), there is provision of financial assistance for upgradation of Government/ Panchayat/ Government aided AYUSH Hospitals and Dispensaries for undertaking addition/ alteration of existing premises, furniture, fixtures, equipment etc. 
• State/UT Governments are eligible for seeking grant-in-aid under this activity as per NAM guidelines.

Hence option 2nd is correct.