A line of symmetry is defined as a line that divides a figure into two parts in a way
such that each part is a mirror image of the other part about that line.
The given figure consists of 16 unit squares arranged as shown. In addition to the
three black squares, what is the minimum number of squares that must be coloured
black, such that both PQ and MN form lines of symmetry? (The figure is
representative)
Options:
(A) 3
(B) 4
(C) 5
(D) 6
M
N P
Q
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2023 Q.5)**
**1. Governing Concept & Domain**:
This question evaluates **Quantitative & Analytical Aptitude** under *General Aptitude* (1 Mark, 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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