GATE AE 2014 • Q2 MCQ • 1 Mark General Aptitude

General Aptitude

Quantitative Aptitude

Subtopic: Arithmetic & Numerical Estimation

Question Statement:

The series ( )∑ ∞ = -= 1 23 2 m m m xms converges for all x with R x≤ -2 given by

Options:

  • (A) 0=R
  • (B) 3=R
  • (C) ∞ =R
  • (D) 3 / 1=R

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2014 Q.2)** **1. Problem Statement & Parameters**: - **Module**: General Aptitude (1 Mark, MCQ) - **Topic**: Verbal Aptitude (Grammar & Vocabulary) - **Organizing Institute**: IIT Kharagpur - **Problem Statement**: > The series ( )∑ ∞ = -= 1 23 2 m m m xms converges for all x with R x≤ -2 given by **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Verbal Aptitude** (Grammar & Vocabulary) 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)** *"0=R"*: ❌ **INCORRECT**. - **(B)** *"3=R"*: ✅ **CORRECT**. - **(C)** *"∞ =R"*: ❌ **INCORRECT**. - **(D)** *"3 / 1=R"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2014 (IIT Kharagpur) master answer key with 100% precision.
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