Which one of the following materials is very hard and very ductile ?

The correct answer is Option 4: Nichrome. In the context of material science within the UPSC syllabus, this question evaluates the unique combination of mechanical and physical properties.

• Nichrome: An alloy of nickel and chromium, it is renowned for its high strength, hardness, and significant ductility. It can be easily drawn into thin wires (ductility) while maintaining structural integrity at high temperatures, making it "very hard" relative to its ability to undergo plastic deformation.
• Carborundum (Silicon Carbide): While extremely hard, it is a ceramic and lacks ductility; it is brittle and will shatter under tension.
• Tungsten: Although it has a high melting point and hardness, it is generally brittle at room temperature and difficult to work with compared to Nichrome.
• Cast Iron: It possesses high compressive strength and hardness but is notoriously brittle due to high carbon content, failing the criteria for ductility.

Therefore, Nichrome is the most suitable choice as it effectively balances high hardness with the high ductility required for industrial heating elements.