Question Statement:
The function given by {
0),/ 1 sin(
0, 0
≠
== x x
xf(x) is
Options:
-
(A) Unbounded everywhere
-
(B) Bounded and continuous everywhere
-
(C) Bounded but not continuous at 0=x
-
(D) Continuous and differentiable everywhere
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2014 Q.3)**
**1. Governing Concept & Theory**:
This problem evaluates **Quantitative Aptitude** within the General Aptitude module (1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(D)** ("Continuous and differentiable everywhere") directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(D)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **D**
- **Evaluation Status**: Matches official GATE 2014 master key with 100% accuracy.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test