Explanation:

The expression 'other authorities' will include all constitutional or statutory authorities on whom powers are conferred for the purpose of promoting economic activities.
In other words, for the purposes of Part III of the constitution, the state comprises of the following:

• Government and Parliament of India i.e the Executive and Legislature of the Union
• Government and Legislature of each State i.e the Executive and Legislature of the various States of India
• All local or other authorities within the territory of India
• All local and other authorities who are under the control of the Government of India

Before understanding what a local authority is, it is important to define Authorities. According to Webster’s Dictionary; “Authority” means a person or body exercising power to command. When read under Article 12, the word authority means the power to make laws (or orders, regulations, bye-laws, notification etc.) which have the force of law. It also includes the power to enforce those laws

• “Local Authority shall mean a municipal committee, district board, body of commissioner or other authority legally entitled to or entrusted by the Government within the control or management of a municipal or local fund.”

Hence option 4th is correct.