Explanation:

All statements are incorrect.

• Education was originally a state subject in India under the Government of India Act 1935. However, during the 42nd Amendment Constitutional Amendment 1976, education was moved to the Concurrent List. 

• Thus now both the central and state governments can legislate on matters concerning education. 

• The 86th Amendment Constitution Act, 2002  made the Right to Education a fundamental right under Article 21A for children aged 6-14 years.

• It added Article 21A under Fundamental Rights, making education a fundamental right for children aged six to fourteen, mandating free and compulsory education.  

• In the Directive Principles of State Policy (DPSP), Article 45 was substituted to emphasize the state's responsibility to provide early childhood care and education until the age of 6. 

• Additionally, Article 51A was amended to include a duty for parents or guardians to ensure educational opportunities for their children or wards between 6 and 14 years. 

Hence option 4th is correct.