GATE BT 2026 • Q12 MCQ • 1 Mark

Section 1: Engineering Mathematics

Engineering Mathematics

Subtopic: Calculus, Linear Algebra & Probability

Question Statement:

Which of the following is one of the eigenvalues for the matrix given below? [3 4 4 -3]

Options:

  • (A) 1
  • (B) 3
  • (C) 5
  • (D) 7

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2026 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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