### **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)** *"$f(x) = x^2
quot;*: ❌ **INCORRECT**.
- **(B)** *"$f(x) = \log x
quot;*: ❌ **INCORRECT**.
- **(C)** *"$f(x) = e^x
quot;*: ❌ **INCORRECT**.
- **(D)** *"$f(x) = \text{constant}
quot;*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.