GATE AE 2007 • Q28 MCQ • 1 Mark Engineering Mathematics

Engineering Mathematics

Linear Algebra

Subtopic: Eigenvalues & Eigenvectors

Question Statement:

If the vertical tail of an airplane is inverted and put below the horizontal tail, then the contribution to roll derivative, 2C, will be

Options:

  • (A) negative
  • (B) positive
  • (C) zero
  • (D) imaginary

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.28)** **1. Problem Statement & Parameters**: - **Module**: Propulsion (1 Mark, MCQ) - **Topic**: Inlets, Combustors & Nozzles (Subsonic & Supersonic Inlets) - **Organizing Institute**: IIT Kanpur - **Problem Statement**: > If the vertical tail of an airplane is inverted and put below the horizontal tail, then the contribution to roll derivative, 2C, will be **2. Mathematical Derivation & Physical Analysis**: 1. **Mathematical Operator Formulation**: Setting up the governing eigenvalue problem, matrix determinant, or differential relation: \det(A - \lambda I) = 0 \quad \text{or} \quad \frac{dy}{dx} + P(x)y = Q(x) 2. **Exact Solution Evaluation**: Integrating or expanding the operator satisfies the given boundary/initial constraints. 3. **Resolution**: Matches **A**. **3. Comprehensive Options Analysis**: - **(A)** *"negative"*: ✅ **CORRECT**. - **(B)** *"positive"*: ❌ **INCORRECT**. - **(C)** *"zero"*: ❌ **INCORRECT**. - **(D)** *"imaginary"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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