• 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

Evaluating the Assertion and Reason concerning Other convenience foods from fruits and vegetables:

The correct answer is Option 2: Both (A) and (R) are true but (R) is NOT the correct explanation of (A).

• Match Instrumentation Transducers with Working Principles:
• Strain Gauge $\longrightarrow$ (I) Mechanical deformation to electrical signal: Piezoresistive sensor whose electrical resistance alters proportionally to mechanical strain ($R \propto \Delta L$).
• Thermocouple $\longrightarrow$ (II) Temperature measurement via Seebeck effect: Generates an electromotive force (EMF) at the junction of two dissimilar metallic conductors proportional to temperature difference.
• LVDT (Linear Variable Differential Transformer) $\longrightarrow$ (III) Precision linear displacement: Inductive transducer converting core linear mechanical position into differential secondary AC voltage with extreme linearity.
• Piezoelectric Transducer $\longrightarrow$ (IV) Electrical charge under mechanical pressure/vibration: Asymmetric crystal (quartz, PZT) generating electric surface charge in response to applied dynamic stress.
• Conclusion: A-I, B-II, C-III, D-IV (Option 2).

Correct option: (2) AA,B-I,C-I,D-V.

• Concept of Thermal Death Time (TDT) Curve:
• Mathematical & Kinetic Definition:
• The TDT curve plots the heating time required to achieve a designated lethal destruction of a microbial population against exposure temperature on semi-logarithmic paper.
• Characterizes the relationship between processing temperature and microbial destruction rate, defining the thermal resistance constant ($z$-value, the temperature change needed to alter the $D$-value by a factor of 10).
• Conclusion: The relationship between temperature and microbial death rate (Option 3).

Correct option: (3) The relationship between temperature and microbial death rate