At a stationary point of a multi-variable function, which of the following is true?
Options:
(A) Curl of the function becomes unity
(B) Gradient of the function vanishes
(C) Divergence of the function vanishes
(D) Gradient of the function is maximum
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.40)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (2 Mark, MCQ)
- **Topic**: Airfoil & Wing Theory (Thin Airfoil Theory & Camber Effects)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> At a stationary point of a multi-variable function, which of the following is true?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Airfoil & Wing Theory** (Thin Airfoil Theory & Camber Effects) under *Aerodynamics & Fluid Mechanics*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Curl of the function becomes unity"*: ❌ **INCORRECT**.
- **(B)** *"Gradient of the function vanishes"*: ✅ **CORRECT**.
- **(C)** *"Divergence of the function vanishes"*: ❌ **INCORRECT**.
- **(D)** *"Gradient of the function is maximum"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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