Subtopic: Permutations, Combinations & Probability
Question Statement:
P
R
In the figure shown above, PQRS is a square. The shaded portion is formed
by the intersection of sectors of circles with radius equal to the side of the
square and centers at S and Q.
The probability that any point picked randomly within the square falls in the
shaded area is
(A)
(B)
(C)
(D)
4-₴
- 1
Options:
(A)
(B)
(C)
(D) 4-₴ - 1
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.9 / GA Q.9)**
**1. Physical Principles & Examination Context**:
- **Topic**: *General Aptitude* (`Verbal & Numerical Ability`) | **Section**: *General Aptitude*
- **Question Type**: **MCQ** | **Marks**: **2 Marks** | **Negative Marks**: **0.67**
- **Governing Principles**: Solved directly by applying fundamental laws of **General Aptitude**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **C**.
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