The factors that determine the nature and size of an industry are I (capital investments), II (business turnover), and IV (power consumption). Therefore, the correct answer is "I, II, and IV."

Let`s break down the factors:

I. Capital investments: The amount of capital invested in an industry plays a crucial role in determining its nature and size. Capital investments are required for setting up infrastructure, purchasing machinery and equipment, and establishing operations. The level of capital investment can indicate the scale and potential growth of an industry.

II. Business turnover: Business turnover refers to the total value of goods or services sold by an industry within a specific period. The turnover can provide insights into the size and economic activity of the industry. Higher turnover generally indicates a larger industry with significant market presence and operations.

IV. Power consumption: Power consumption is an important factor in determining the nature and size of an industry. Industries that require high levels of power consumption, such as manufacturing or heavy industries, tend to have larger physical infrastructures and operations. Power consumption can also indicate the energy intensity and production capacity of an industry.

III. Labour force: While the labor force is an essential component of an industry, it is not specifically mentioned as a factor determining the nature and size of the industry in the given options. The size of the labor force is related to the employment opportunities and the workforce required to meet the industry`s operations and production needs. However, it is not directly included in the factors provided in the options.

Therefore, based on the given options, the factors that determine the nature and size of the industry are I (capital investments), II (business turnover), and IV (power consumption).