The correct answer is option 'C' - The Planning Commission was set up by a Cabinet Resolution.

The Planning Commission of India was an institution established to formulate and oversee the country's Five-Year Plans. It played a crucial role in the development and economic planning of India. Let's delve into the details of its establishment and functioning:

1. Background:
- After India's independence in 1947, the country faced numerous challenges in terms of poverty, unemployment, and economic backwardness.
- To address these issues and accelerate economic growth, the need for a centralized planning body was recognized.

2. Establishment:
- In 1950, the Indian government established the Planning Commission through a Cabinet Resolution.
- The resolution outlined the objectives and functions of the Planning Commission.
- The Commission was given the responsibility of formulating and implementing comprehensive economic plans to promote balanced and sustainable development across various sectors of the economy.

3. Composition:
- The Planning Commission was composed of a Chairman, who was usually the Prime Minister, and a set of full-time and part-time members.
- The members were experts from different fields such as economics, agriculture, industry, social welfare, etc.
- State Chief Ministers and Union Ministers for key sectors were also included as ex-officio members.

4. Functions:
- The Commission's primary function was to prepare Five-Year Plans. These plans set targets and priorities for various sectors of the economy.
- It conducted detailed studies and assessments of the country's resources, infrastructure, and potential for growth.
- The Commission allocated resources and funds to different sectors based on their importance and priority.
- It also monitored the progress of plan implementation and evaluated the outcomes achieved.

5. Role and Impact:
- The Planning Commission played a pivotal role in shaping India's economic policies and development strategies.
- It coordinated efforts between the central and state governments, and between different sectors, to achieve planned economic growth.
- The Commission's plans and policies helped in reducing poverty, improving infrastructure, promoting industrialization, and enhancing social welfare.
- However, over time, criticisms arose regarding the Commission's centralized planning approach, leading to its eventual dissolution in 2014.

In conclusion, the Planning Commission of India was established by a Cabinet Resolution in 1950. It played a crucial role in formulating and implementing Five-Year Plans to promote economic growth and development in the country.