GATE AE 2011 • Q2 MCQ • 1 Mark General Aptitude

General Aptitude

Quantitative Aptitude

Subtopic: Arithmetic & Numerical Estimation

Question Statement:

Which of the following functions is periodic?

Options:

  • (A) f(x) = x^2
  • (B) f(x) = log x
  • (C) f(x) = e^x
  • (D) f(x) = const.

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.2)** **1. Problem Statement & Parameters**: - **Module**: General Aptitude (1 Mark, MCQ) - **Topic**: Verbal Aptitude (Grammar & Vocabulary) - **Organizing Institute**: IIT Madras - **Problem Statement**: > Which of the following functions is periodic? **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 **D**. **3. Comprehensive Options Analysis**: - **(A)** *"$f(x) = x^2$"*: ❌ **INCORRECT**. - **(B)** *"$f(x) = \log x$"*: ❌ **INCORRECT**. - **(C)** *"$f(x) = e^x$"*: ❌ **INCORRECT**. - **(D)** *"$f(x) = \text{constant}$"*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
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