GATE BT 2022 • Q12
MCQ • 1 Mark
Section 1: Engineering Mathematics
Engineering Mathematics
Subtopic: Calculus, Linear Algebra & Probability
Question Statement:
If the eigenvalues of a 2 ×2 matrix P are 4 and 2, then the eigenvalues of the
matrix 1P are
Options:
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(A) 0.01
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(B) 1.0
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(C) 4.6
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(D) 100.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2022 Q.12)**
**1. Governing Concept & Domain**:
This question evaluates **Engineering Mathematics** under *Section 1: Engineering Mathematics* (1 Mark, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Engineering Mathematics.
- 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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