• Extended Surface (Fin) Geometries in Heat Exchangers:
• Fins expand convective heat transfer surface area ($q = h A \Delta T$):
• (I) Longitudinal fins: Rectangular profiles attached along planar furnace or heat exchanger walls.
• (II) Radial (annular) fins: Concentric circular discs around cylindrical evaporator/condenser pipes.
• (III) Conical pin fins (spines): Protruding tapered rods maximizing heat dissipation with minimum fin weight.
• All three are standard, mathematically valid fin geometries.
• Conclusion: (I), (II) and (III) (Option 1).

Correct option: (1) 0), () and (I!)

• Arrangement of Physical Constants by Increasing Magnitude:
• Evaluating the numerical magnitude of each physical constant in standard SI units:
• Planck's Constant ($h$): $h \approx 6.626 \times 10^{-34}\ \text{J}\cdot\text{s}$ (Order of magnitude: $10^{-34}$)
• Stefan-Boltzmann Constant ($\sigma$): $\sigma \approx 5.670 \times 10^{-8}\ \text{W}\cdot\text{m}^{-2}\cdot\text{K}^{-4}$ (or $\text{kg}\cdot\text{s}^{-3}\cdot\text{K}^{-4}$, Order of magnitude: $10^{-8}$)
• Universal Gas Constant ($R$): $R \approx 8.314\ \text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$ (Order of magnitude: $10^{0} \approx 8.31$)
• Speed of Light in Vacuum ($c$): $c \approx 2.998 \times 10^{8}\ \text{m/s}$ (Order of magnitude: $10^{8}$)
• Ranking by Numerical Value:

• Conclusion: The increasing order of magnitude is B, A, D, C (Option 1).

Correct option: (1) B,A,D,C