Step 1: Link density to structure
Low density means loose packing, which comes from side branches.
Step 2: Identify
This is LDPE, made by a free radical process under high pressure.
Step 3: Others
HDPE is linear, PVC is linear and melamine-formaldehyde is a cross-linked network polymer.
Step 4: Answer
Option (B).
Step 5: Why the others are not branched
High density polythene is made with Ziegler-Natta catalysts, and its chains stay straight, so they pack closely and the density is higher. PVC is formed by addition of vinyl chloride along one chain. Melamine joins with formaldehyde into a cross-linked network, where different chains are tied together, which is a different category from simple branching.
Final Answer:
LDPE is the branched polymer. This is option (B).
\[ \boxed{\text{(B) }\text{Low density polythene}} \]