GATE AE 2013 • Q3 MCQ • 1 Mark General Aptitude

General Aptitude

Quantitative Aptitude

Subtopic: Arithmetic & Numerical Estimation

Question Statement:

At 0x , the function y x is

Options:

  • (A) continuous but not differentiable
  • (B) continuous and differentiable
  • (C) not continuous but differentiable
  • (D) not continuous and not differentiable

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.3)** **1. Problem Statement & Parameters**: - **Module**: General Aptitude (1 Mark, MCQ) - **Topic**: Quantitative Aptitude (Arithmetic & Numerical Estimation) - **Organizing Institute**: IIT Bombay - **Problem Statement**: > At 0x , the function y x is **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Quantitative Aptitude** (Arithmetic & Numerical Estimation) 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 **A**. **3. Comprehensive Options Analysis**: - **(A)** *"continuous but not differentiable"*: ✅ **CORRECT**. - **(B)** *"continuous and differentiable"*: ❌ **INCORRECT**. - **(C)** *"not continuous but differentiable"*: ❌ **INCORRECT**. - **(D)** *"not continuous and not differentiable"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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