The resistance if a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be:

Step 1: Resistance in terms of Volume and Length
We know that Resistance: R = ρ l/A
R = ρ l²/V (∵V = A l )
When the wire is melted, its volume remains constant.
Also, since the material is same, therefore resistivity ρ is also constant.
Hence, R ∝ l²
Step 2: Ratio of initial and final Resistances
R₁/R₂ = (l₁/l₂)² (ρ = constant)
R₂ = (l₂/l₁)² R₁ = (n l₁/l₁)² R = n²R
Therefore, New Resistance = n²R