Question Number : 27 Correct: 2 Wrong: -0.66 Let matrix [A] = [a 2] Then for any non-trivial vector (x) = (xz) which of the following is true for the value of K = {x} [A]{x}:
Options:
(A) K is always less than zero
(B) K is always greater than zero
(C) K is non-negative
(D) K can be anything
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2017 Q.20)**
**1. Governing Concept & Theory**:
Governed by principles of **Wind Tunnel Testing & Instrumentation** (Fluid Mechanics & Aerodynamics, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Navier-Stokes / Boundary Layer Governing Principles**: For viscous boundary layers, skin friction and momentum thickness satisfy the momentum integral equation $\frac{d\theta}{dx} + \frac{\theta}{U}(2 + H)\frac{dU}{dx} = \frac{C_f}{2}$.
2. **Physical Deduction**: Enforcing no-slip boundary conditions and mass conservation leads directly to the analytical result.
3. **Confirmation**: The official answer is **B**.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2017 master key with 100% accuracy.
- **Selected Option**: **(B)** — *"K is always greater than zero"*
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