The correct answer is option 3, Iron and Steel industry. This industry is considered the "mother industry" because it forms the bedrock of all industrial activities. Iron and steel are essential materials used in various sectors such as construction, automotive, aerospace, and manufacturing.

Option 1, Petro-chemical industry, is not the correct answer because while it is an important industry, it is not referred to as the "mother industry."

Option 2, Cement industry, is also not the correct answer. Though cement is a crucial material in the construction sector, it is not considered the "mother industry" as it does not have the same level of significance in all industrial activities.

Option 4, Fertilizer industry, is not the correct answer as it is not considered the "mother industry." The fertilizer industry plays a significant role in agriculture, but it is not as fundamental as the iron and steel industry.

Therefore, option 3 is the correct answer.