GATE AE 2010 • Q30 MCQ • 1 Mark Engineering Mathematics

Engineering Mathematics

Numerical Methods

Subtopic: Newton-Raphson Method

Question Statement:

Newton-Raphson method achieves an order of convergence equal to:

Options:

  • (A) 1.0
  • (B) 1.67
  • (C) 2.0
  • (D) 2.5

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.30)** **1. Problem Statement & Parameters**: - **Module**: Propulsion (1 Mark, MCQ) - **Topic**: Rocket Propulsion (Tsiolkovsky Rocket Equation & Specific Impulse) - **Organizing Institute**: IIT Guwahati - **Problem Statement**: > Newton-Raphson method achieves an order of convergence equal to: **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Rocket Propulsion** (Tsiolkovsky Rocket Equation & Specific Impulse) under *Propulsion*. 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)** *"1.0"*: ❌ **INCORRECT**. - **(B)** *"1.67"*: ✅ **CORRECT**. - **(C)** *"2.0"*: ❌ **INCORRECT**. - **(D)** *"2.5"*: ❌ **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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