GATE BT 2024 • Q29
MCQ • 1 Mark
Section 2: General Biotechnology
Biochemistry, Microbiology & Molecular Biology
Subtopic: Enzyme Kinetics, Cell Biology & Metabolism
Question Statement:
The value of the series 1+ sin x + cos2 x + sin3 x + ⋯ at x =
𝜋
4 is ________.
Options:
-
(A) 1
√2+1
-
(B) √2
√2+1
-
(C) 1
√2-1
-
(D) √2
√2-1
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2024 Q.29)**
**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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