GATE BT 2024 • Q28 MCQ • 1 Mark

Section 2: General Biotechnology

Biochemistry, Microbiology & Molecular Biology

Subtopic: Enzyme Kinetics, Cell Biology & Metabolism

Question Statement:

A value of k for which the linear equations (k - 1)x + 3y = 0 and 2x + ky = 0 have a non-zero solution is ________.

Options:

  • (A) 1
  • (B) 2
  • (C) 3
  • (D) 4

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2024 Q.28)** **1. Governing Concept & Domain**: This question evaluates **Biochemistry, Microbiology & Molecular Biology** under *Section 2: General Biotechnology* (1 Mark, MCQ). **2. Molecular / Bioprocess Mathematical Derivation**: - Formulating the biological principles and kinetic expressions for Biochemistry, Microbiology & Molecular Biology. - Applying governing bioprocess and biochemical equations: $v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$ - Deductive verification establishes option **(C)** as the correct solution. **3. Final Answer**: Correct Option is **(C)**.

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