In general, the properties that decrease and increase down a group in the periodic table, respectively, are:

🧠 Down a group: atomic radius INCREASES (extra shells); electronegativity DECREASES (electrons farther from nucleus) The question wants two properties — one that decreases down a group, and one that increases. The first slot is the decreasing property; the second slot is the increasing one.

🗺️ Check each property's trend down a group Atomic radius: each new period adds a shell → radius increases down. ↑ Electronegativity: bigger atom holds bonded electrons less tightly → decreases down. ↓ Electron gain enthalpy: usually decreases in magnitude down (with halogen anomalies) → not strictly increasing. Mostly decreasing.

Match options: (a) atomic radius (decreases — wrong), electronegativity (increases — wrong). ✗ (b) electronegativity (decreases ✓), atomic radius (increases ✓). ✓ (c) electronegativity (decreases ✓), electron gain enthalpy (decreases — should be increases). ✗ (d) electron gain enthalpy (decreases ✓), electronegativity (decreases — should be increases). ✗

So option (b) is the only consistent pair.

⚠️ The trap Option (a) flips the order — atomic radius is in the "decreases" slot but it actually INCREASES down a group. Read the slot order: "properties that decrease and increase down a group, respectively". The first listed property must decrease, the second must increase. Atomic radius can never go in the "decreases" slot.

$\boxed{\text{Answer: (b)}}$