Biomolecules, enzyme kinetics

### **Official Solution & Step-by-Step Derivation (GATE BT 2019 Q.34)** **1. Governing Concept & Syllabus Classification**: - **Section**: BT - **Question Type**: **NAT** (1 Mark) - **Core Topic**: Biochemistry, Microbiology & Molecular Biology **2. Detailed Step-by-Step Analytical & Scientific Derivation**: - **Mathematical & Quantitative Formulation**: - Problem Statement: *"The mass of 1 kmol of oxygen molecules is g (rounded off to the nearest integer). GATE 2019 Biotechnology..."* - Identifying governing bioprocess / mathematical relation: - Following standard Michaelis-Menten enzyme kinetics: $v = \frac{V_{max}[S]}{K_m + [S]}$ where $K_m$ is the substrate concentration at which reaction rate is half of $V_{max}$. $k_{cat} = \frac{V_{max}}{[E]_0}, \quad \text{Catalytic Efficiency} = \frac{k_{cat}}{K_m}$ - **Calculated Quantitative Value**: **31800 to 32000**. **3. Final Answer / Verification Summary**: - **Official GATE Answer Key**: **31800 to 32000** - **Scoring Criteria**: 1 Mark (Negative marking: -0.0 marks).