• Chain Length vs Melting Point of Saturated Fatty Acids: In unbranched saturated fatty acids, melting point increases systematically with increasing carbon chain length due to greater surface area and cumulative London dispersion forces:
• Lauric acid (12:0): $\text{CH}_3(\text{CH}_2)_{10}\text{COOH} \rightarrow$ $44.2^\circ\text{C}$ (III)
• Myristic acid (14:0): $\text{CH}_3(\text{CH}_2)_{12}\text{COOH} \rightarrow$ $53.9^\circ\text{C}$ (II)
• Palmitic acid (16:0): $\text{CH}_3(\text{CH}_2)_{14}\text{COOH} \rightarrow$ $63.1^\circ\text{C}$ (IV)
• Stearic acid (18:0): $\text{CH}_3(\text{CH}_2)_{16}\text{COOH} \rightarrow$ $69.6^\circ\text{C}$ (I)
• Systematic Match: (A)-(III), (B)-(IV), (C)-(II), (D)-(I) (Option 4).

Correct option: (4) (A) - (Ill), (B) - (VY), (C)- (I), (2) - (1)

• Statement (I) is False: The hydrophobic, non-polar hydrocarbon tail of fatty acids provides high solubility in non-polar organic solvents (chloroform, hexane, diethyl ether, benzene) and explains their insolubility in polar aqueous solutions.
• Statement (II) is True: As fatty acyl chain length increases and degree of unsaturation decreases, hydrophobic surface area increases and crystal packing tightens, progressively decreasing solubility in water.
• Conclusion: Statement (I) is false but Statement (II) is true.

Correct option: (4) Statement (I) is false but Statement ({I) is true.

• Ubiquinone (Coenzyme Q): A fat-soluble benzoquinone containing an isoprenoid side chain (10 isoprene units in humans, $Q_{10}$; 9 in rodents, $Q_9$) that functions as a mobile electron and proton shuttle between Complex I/II and Complex III in the inner mitochondrial membrane.
• Distinction from Other Quinones: Plastoquinone functions in chloroplast photosynthesis; Phylloquinone is Vitamin $\text{K}_1$; Menaquinone is Vitamin $\text{K}_2$.

Correct option: (3) Ubiquinone

• Statement (B) is Correct: Pyruvate decarboxylase requires Thiamine pyrophosphate (TPP) and $\text{Mg}^{2+}$ as essential cofactors to stabilize the carbanion intermediate.
• Statement (D) is Correct: Catalyzes the decarboxylation of pyruvate to acetaldehyde and carbon dioxide:

• Statement (E) is Correct: The decarboxylation reaction is physiologically irreversible.
• Why (A) and (C) are Incorrect: Acetyl-CoA is the allosteric activator of pyruvate carboxylase (gluconeogenesis), not decarboxylase. Pyruvate decarboxylase is active in plants, fungi, and yeasts for ethanol fermentation, but is absent in animals.
• Conclusion: (B), (D), and (E) only are correct.

• Isocitrate Partitioning Control: In organisms capable of utilizing acetate/fatty acids (e.g., germinating oilseeds, E. coli), isocitrate can enter the energy-generating citric acid cycle or the biosynthetic glyoxylate cycle.
• Enzymatic Switch: The metabolic flux is regulated by the reversible phosphorylation of Isocitrate dehydrogenase (ICDH). Phosphorylation inactivates ICDH, diverting isocitrate into the glyoxylate cycle via isocitrate lyase to produce succinate and malate for gluconeogenesis.

Correct option: (2) Isocitrate dehydrogenase