The Railways are considered the largest public sector undertaking in India. The Indian Railways is a massive network that plays a crucial role in the country's transportation system, connecting cities, towns, and villages across the nation. It is one of the largest employers in the country and handles millions of passengers and goods daily. Here's why the other options are incorrect:
- Option (1): Petroleum: While the petroleum sector is significant, it does not encompass as many employees or infrastructure as the railways.
- Option (2): Airways: The aviation sector, including airlines like Air India, is important but is much smaller in scale compared to the railways.
- Option (3): Railways: This is the correct answer, as the Indian Railways is the largest public sector undertaking in terms of size, workforce, and infrastructure.
- Option (4): Roadways: The road transport sector is extensive but is primarily managed by state governments and private entities, making it less centralized compared to the railways.
Answer: $\boxed{\text{Railways}}$