<p>The maximum number of points of intersection of five lines and four circles is</p>
Step-by-Step Solution
Key Concept: Count all possible pairwise intersections: lines with lines, lines with circles, and circles with circles. Each pair has a maximum number of intersection points that must be calculated separately.
<p><strong>Step 1: Line-Line intersections</strong></p><p>Number of ways to choose 2 lines from 5 = C(5,2) = 10</p><p>Each pair of lines intersects at maximum 1 point</p><p>Maximum points = 10 × 1 = 10</p><p><strong>Step 2: Line-Circle intersections</strong></p><p>Number of line-circle pairs = 5 × 4 = 20</p><p>Each line intersects a circle at maximum 2 points</p><p>Maximum points = 20 × 2 = 40</p><p><strong>Step 3: Circle-Circle intersections</strong></p><p>Number of ways to choose 2 circles from 4 = C(4,2) = 6</p><p>Each pair of circles intersects at maximum 2 points</p><p>Maximum points = 6 × 2 = 12</p><p><strong>Step 4: Total intersection points</strong></p><p>Maximum = 10 + 40 + 12 = <strong>62</strong></p><p>∴ Answer: D</p>
Correct Answer: D