GATE AE 2012 • Q64 MCQ • 2 Marks Aerospace Structures

Aerospace Structures

Aerospace Materials & Fatigue

Subtopic: Fatigue Crack Growth & S-N Curves

Question Statement:

Two points (4, p) and (0, q) lie on a straight line having a slope of 3/4. The value of (p - q) is:

Options:

  • (A) -3
  • (B) 0
  • (C) 3
  • (D) 4

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.64)** **1. Problem Statement & Parameters**: - **Module**: Aerospace Structures (2 Mark, MCQ) - **Topic**: Aerospace Materials & Fatigue (Aluminum, Titanium & Aerospace Alloys) - **Organizing Institute**: IIT Delhi - **Problem Statement**: > Two points (4, p) and (0, q) lie on a straight line having a slope of 3/4. The value of (p - q) is: **2. Mathematical Derivation & Physical Analysis**: 1. **Linear Coordinate Geometry**: The slope $m$ of a line passing through points $(x_1, y_1) = (4, p)$ and $(x_2, y_2) = (0, q)$ is: m = \frac{y_1 - y_2}{x_1 - x_2} = \frac{p - q}{4 - 0} = \frac{p - q}{4} 2. **Equating with Given Slope**: \frac{p - q}{4} = \frac{3}{4} \implies p - q = 3 Matches **Option (C)** (3). **3. Comprehensive Options Analysis**: - **(A)** *"-3"*: ❌ **INCORRECT**. - **(B)** *"0"*: ❌ **INCORRECT**. - **(C)** *"3"*: ✅ **CORRECT**. - **(D)** *"4"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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