GATE AE 2010 • Q49
MCQ • 2 Marks
Flight Mechanics & Space Dynamics
Static Stability & Control
Subtopic: Static Margin & Stick-Fixed/Free Stability
Question Statement:
Core digits 2, 2. 3. 3. 3. 4. 4. 4. 4 how many distinct digit numbers greater than 3000 can be
Options:
-
(A) 50
-
(B) 51
-
(C) 52
-
(D) 54
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.49)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Static Stability & Control (Static Margin & Stick-Fixed/Free Stability)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> Core digits 2, 2. 3. 3. 3. 4. 4. 4. 4 how many distinct digit numbers greater than 3000 can be
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Static Stability & Control** (Static Margin & Stick-Fixed/Free Stability) under *Flight Mechanics & Space Dynamics*. 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)** *"50"*: ❌ **INCORRECT**.
- **(B)** *"51"*: ✅ **CORRECT**.
- **(C)** *"52"*: ❌ **INCORRECT**.
- **(D)** *"54"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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