• ⚠️ Note: This question was officially DROPPED by NTA/ICAR in the final answer key because the mathematically calculated ionic strength ($0.16\text{ M}$) was omitted from the answer options. Full marks were awarded to all candidates.
• Calculation of Ionic Strength ($I$) of Electrolyte Solutions:
• The Lewis-Randall formula for ionic strength is:

• For $0.02\text{ M } \text{BaCl}_2$:
• $\text{Ba}^{2+}$: $c = 0.02\text{ M},\ z = +2 \implies c z^2 = 0.02 \times 4 = 0.08$
• $\text{Cl}^-$: $c = 0.04\text{ M},\ z = -1 \implies c z^2 = 0.04 \times 1 = 0.04$
• Subtotal for $\text{BaCl}_2 = \frac{1}{2}(0.08 + 0.04) = 0.06\text{ M}$
• For $0.1\text{ M } \text{HCl}$:
• $\text{H}^+$: $c = 0.1\text{ M},\ z = +1 \implies c z^2 = 0.1 \times 1 = 0.10$
• $\text{Cl}^-$: $c = 0.1\text{ M},\ z = -1 \implies c z^2 = 0.1 \times 1 = 0.10$
• Subtotal for $\text{HCl} = \frac{1}{2}(0.10 + 0.10) = 0.10\text{ M}$
• Total Ionic Strength:

• Discrepancy Note: The examination options listed 0.80, 0.70, 0.65, and 0.60. Since the correct value $0.16\text{ M}$ was not available, NTA dropped the question.

• Essential Plant Nutrients and Specific Physiological Roles:
• Boron (B): Essential for cis-diol borate ester complexation, cell wall cross-linking (rhamnogalacturonan II), and sugar translocation / pollen tube germination $\rightarrow$ (I)
• Phosphorus (P): Key component of high-energy pyrophosphate bonds (ATP/ADP) and phosphodiester backbones in DNA/RNA $\rightarrow$ (II)
• Potassium (K): Primary osmoticum governing stomatal guard cell turgor and allosteric cofactor for $\gt 60$ metabolic enzymes $\rightarrow$ (III)
• Zinc (Zn): Catalytic cofactor for carbonic anhydrase and essential activator for auxin (indole-3-acetic acid) synthesis from tryptophan $\rightarrow$ (IV)
• Systematic Match: (A)-(I), (B)-(II), (C)-(III), (D)-(IV) corresponds to Option 1.

Correct option: (1) (A) - (III), (B) - (IV), (C) - (W), (D) -