Question Statement:
All other factors remaining constant, if the weight of an aircraft increases by 30% then the takeoff distance increases by approximately:
Options:
-
(A) 15%
-
(B) 30%
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(C) 70%
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(D) 105%
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.4)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Analytical & Spatial Aptitude (Deductive Logic & Syllogisms)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> All other factors remaining constant, if the weight of an aircraft increases by 30% then the takeoff distance increases by approximately:
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Analytical & Spatial Aptitude** (Deductive Logic & Syllogisms) under *General Aptitude*. 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)** *"15%"*: ❌ **INCORRECT**.
- **(B)** *"30%"*: ✅ **CORRECT**.
- **(C)** *"70%"*: ❌ **INCORRECT**.
- **(D)** *"105%"*: ❌ **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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