Symmetric airfoils only. (C) Any airfoil shape. (B) Cambered airfoils only. (D) Joukowski airfoils only. Q.5 The ordinary differential equation ds? + ky = 0 where k is real and positive
Options:
(A) is non-linear
(B) has a characteristic equation with one real and one complex root
(C) has a characteristic equation with two real roots
(D) has a complementary function that is simple harmonic
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2009 Q.3)**
**1. Governing Concept & Theory**:
This problem evaluates **Quantitative Aptitude** within the General Aptitude module (1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(A)** (`is non-linear`) directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(A)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2009 master key with 100% accuracy.
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