GATE AE 2009 • Q5 MCQ • 1 Mark General Aptitude

General Aptitude

Quantitative Aptitude

Subtopic: Arithmetic & Numerical Estimation

Question Statement:

The propulsive efficiency of a turbo-jet engine moving at velocity Uo and having exhaust velocity Ue with respect to the engine is given by

Options:

  • (A) 2 Uoo/Ve +1 U
  • (B) 1-
  • (C) 20. Ve
  • (D) 2000

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.5)** **1. Problem Statement & Parameters**: - **Module**: General Aptitude (1 Mark, MCQ) - **Topic**: Analytical & Spatial Aptitude (Spatial Reasoning & Paper Folding) - **Organizing Institute**: IIT Roorkee - **Problem Statement**: > The propulsive efficiency of a turbo-jet engine moving at velocity Uo and having exhaust velocity Ue with respect to the engine is given by **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Analytical & Spatial Aptitude** (Spatial Reasoning & Paper Folding) 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 **D**. **3. Comprehensive Options Analysis**: - **(A)** *"2 Uoo/Ve +1 U"*: ❌ **INCORRECT**. - **(B)** *"1-"*: ❌ **INCORRECT**. - **(C)** *"20. Ve"*: ❌ **INCORRECT**. - **(D)** *"2000"*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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