GATE BT 2026 • Q27
MCQ • 1 Mark
Section 2: General Biotechnology
Biochemistry, Microbiology & Molecular Biology
Subtopic: Enzyme Kinetics, Cell Biology & Metabolism
Question Statement:
The equation
d2y
dx2 - y = 0 has a solution of the form y = e Ax. The value(s) of
A satisfying this is/are:
Options:
-
(A) 0
-
(B) 1
-
(C) -1
-
(D) -∞
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2026 Q.27)**
**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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