Subtopic: Free & Forced Vibrations of Continuous Beams
Question Statement:
Following table gives data on tourists from different countries visiting India in the year 2011.
Country Number of
Tourists
USA 2000
England 3500
Germany 1200
Italy 1100
Japan 2400
Australia 2300
France 1000
Which two countries contributed to the one third of the total number of tourists who visited India in
2011?
Options:
(A) USA and Japan
(B) USA and Australia
(C) England and France
(D) Japan and Australia
2013 AEROSPACE ENGINEERING - AE
AE 19/19
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.63)**
**1. Problem Statement & Parameters**:
- **Module**: Aerospace Structures (2 Mark, MCQ)
- **Topic**: Structural Dynamics & Aeroelasticity (Free & Forced Vibrations of Continuous Beams)
- **Organizing Institute**: IIT Bombay
- **Problem Statement**:
> Following table gives data on tourists from different countries visiting India in the year 2011. Country Number of Tourists USA 2000 England 3500 Germany 1200 Italy 1100 Japan 2400 Australia 2300 France 1000 Which two countries contributed to the one third of the total number of tourists who visited India in 2011?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Structural Dynamics & Aeroelasticity** (Free & Forced Vibrations of Continuous Beams) under *Aerospace Structures*. 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"USA and Japan"*: ❌ **INCORRECT**.
- **(B)** *"USA and Australia"*: ❌ **INCORRECT**.
- **(C)** *"England and France"*: ✅ **CORRECT**.
- **(D)** *"Japan and Australia
2013 AEROSPACE ENGINEERING - AE
AE 19/19"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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