Indian Petrochemicals Corporation Limited is not a public-sector undertaking.

Explanation:
Public sector undertakings (PSUs) are government-owned corporations or companies in which the government has a majority stake. These companies are established to provide essential goods and services to the public and contribute to the economic development of the country. They are often involved in industries such as transportation, energy, telecommunications, and manufacturing.

In the given options:
a) Pawan Hans Limited: Pawan Hans Limited is a public-sector undertaking and is a helicopter service company owned by the Government of India. It provides helicopter transportation services for various purposes including offshore operations, charter services, and medical evacuation.

b) Rail Vikas Nigam: Rail Vikas Nigam Limited is also a public-sector undertaking and is responsible for the development and implementation of railway infrastructure projects. It is involved in activities such as construction of new railway lines, doubling and electrification of existing lines, and setting up of railway bridges.

c) Air India Express Limited: Air India Express Limited is a subsidiary of Air India and is a public-sector undertaking. It operates as a low-cost airline and provides international flight services to various destinations.

d) Indian Petrochemicals Corporation Limited: Indian Petrochemicals Corporation Limited is a private-sector company and not a public-sector undertaking. It is a subsidiary of Reliance Industries Limited and is involved in the production and sale of petrochemical products.

In conclusion, out of the given options, Indian Petrochemicals Corporation Limited is the company that is not a public-sector undertaking.