GATE BT 2016 • Q17 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Fundamentals of Linear Algebra

Question Statement:

Fed batch cultivation is suitable for which of the following? P. Processes with substrate inhibition Q. Processes with product inhibition R. High cell density cultivation (A) P and Q only (B) P and R only (C) Q and R only (D) P, Q and R

Options:

  • (A) P and Q only
  • (B) P and R only
  • (C) Q and R only
  • (D) P, Q and R

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.17)** **1. Governing Concept & Question Classification**: - **Section**: BT - **Question Type**: **MCQ** (1 Mark) - **Topic**: Biochemistry / Bioenergetics (Chemiosmotic Hypothesis & ATP Synthase Topology) **2. Detailed Step-by-Step Analysis**: - According to Peter Mitchell's **Chemiosmotic Theory**: 1. The electron transport chain (Complexes I, III, and IV) actively pumps protons ($H^+$) from the **mitochondrial matrix** across the inner mitochondrial membrane into the **intermembrane space**. 2. This generates a proton motive force ($\Delta p$) characterized by a higher proton concentration (lower pH, positive charge) in the intermembrane space and a lower proton concentration (higher pH, negative charge) in the matrix. 3. The $F_o F_1$-ATP synthase complex is embedded in the inner mitochondrial membrane: - The hydrophobic $F_o$ proton channel spans the inner membrane. - The catalytic $F_1$ headpiece ($\alpha_3\beta_3$ hexamer) projects into the **mitochondrial matrix**. 4. Protons flow down their electrochemical gradient from the **intermembrane space into the matrix** through $F_o$, driving mechanical rotation of the $\gamma$ stalk, which synthesizes ATP from ADP and $P_i$ on the $F_1$ catalytic sites in the **mitochondrial matrix**. - Therefore, $F_1$ is located in the **mitochondrial matrix**. - **Option-by-Option Evaluation**: - **Option (A) [INCORRECT]**: $F_1$ is not on the outer membrane. - **Option (B) [CORRECT]**: The catalytic $F_1$ subunit of ATP synthase faces and resides within the mitochondrial matrix. - **Option (C) [INCORRECT]**: The intermembrane space contains the $H^+$ reservoir, but $F_1$ extends into the matrix. - **Option (D) [INCORRECT]**: $F_1$ does not project into the cytoplasm. **3. Final Answer / Verification Summary**: - **Official GATE Answer Key**: **B** - **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).

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