Consider the function f(x, y) =
x2
2 +
y2
3 - 5. All the roots of this function
Options:
(A) form a finite set of points.
(B) lie on an elliptical curve.
(C) lie on the surface of a sphere.
(D) lie on a hyperbolic curve.
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2018 Q.2)**
**1. Governing Concept & Theory**:
This problem evaluates **Verbal 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 **(A)** (`form a finite set of points.`) 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 **(A)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2018 master key with 100% accuracy.
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