Question Statement:
The coefficient of x4 in the polynomial (x - 1)3(x - 2)3 is equal to _______.
Options:
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(A) 33
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(B) ̶ 3
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(C) 30
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(D) 21
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2023 Q.9)**
**1. Governing Concept & Domain**:
This question evaluates **Quantitative & Analytical Aptitude** under *General Aptitude* (2 Marks, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Quantitative & Analytical Aptitude.
- 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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