A circle with center at (x, y) = (0.5, 0) and radius = 0.5 intersects with another
circle with center at (x, y) = (1, 1) and radius = 1 at two points. One of the points
of intersection (x, y) is:
Options:
(A) (0, 0)
(B) (0.2, 0.4)
(C) (0.5, 0.5)
(D) (1, 2)
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2025 Q.9)**
**1. Governing Concept & Domain**:
This question evaluates **Quantitative & Analytical Aptitude** under *General Aptitude* (2 Marks, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Quantitative & Analytical Aptitude.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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