In the open-loop process shown in the figure, the input U(s), the transfer function
Gp(s) and the output Y(s) are given in the Laplace domain in terms of the Laplace
variable s. For this process, which of the following is true?
(where M, šp, KP, are the magnitude of the input, the characteristic time and the gain
for the process, respectively)
Options:
(A) y(t) = Kp(1 - e-t špā )
(B) y(t) = MKp(1 - e-t špā )
(C) y(t) = Kp(M - e-t špā )
(D) y(t) = Kp(1 - Me-t špā )
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2026 Q.36)**
**1. Governing Concept & Domain**:
This question evaluates **Biochemistry, Microbiology & Molecular Biology** under *Section 2: General Biotechnology* (2 Marks, 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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