The solution to the following set of equations is
2xx + 3yy = 4
4xx + 6yy = 0
(A) x=0, y=0 (B) x=2, y=0 (C) 4x= -6y (D) No solution
Options:
(A) x=0, y=0
(B) x=2, y=0
(C) 4x= -6y
(D) No solution
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2014 Q.5)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: GA
- **Question Type**: **MCQ** (1 Mark)
- **Core Topic**: Quantitative & Analytical Aptitude
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"The population of a new city is 5 million and is growing at 20% annually. How many years would
it take to double at this growth rate?..."*
- **Option (A) [CORRECT]**: *"3-4 years"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (B) [INCORRECT]**: *"4-5 years"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"5-6 years"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"6-7 years
Q. 6 – Q. 10 carry two marks each."* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.33 marks).
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