Selection Of Consecutive Objects
From 20 points placed on a straight line, the number of line segments that can be formed by joining any two of these points equals which value?
Select the correct option:
Solution
190
A line segment is determined by an unordered pair of distinct points, so the count is a simple combination, a basic JEE Advanced application. With 20 points, the number of ways to choose 2 of them is C(20, 2) = (20 × 19)/2 = 190. Each chosen pair gives exactly one segment, and order does not matter since the segment from P to Q is the same as from Q to P. Option 400 = 20^2 counts ordered pairs including a point with itself. Option 20 counts only the points. Option 380 = 20 × 19 counts ordered pairs of distinct points, double counting each segment. Hence there are 190 segments. Plausibility check: dividing the ordered count 20 × 19 = 380 by 2 to remove direction gives 190, matching the combination C(20,2) and confirming that each unordered pair yields one segment.
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About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- selection of consecutive objects
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
190
A line segment is determined by an unordered pair of distinct points, so the count is a simple combination, a basic JEE Advanced application. With 20 points, the number of ways to choose 2 of them is C(20, 2) = (20 × 19)/2 = 190. Each chosen pair gives exactly one segment, and order does not matter since the segment from P to Q is the same as from Q to P. Option 400 = 20^2 counts ordered pairs including a point with itself. Option 20 counts only the points. Option 380 = 20 × 19 counts ordered pairs of distinct points, double counting each segment. Hence there are 190 segments. Plausibility check: dividing the ordered count 20 × 19 = 380 by 2 to remove direction gives 190, matching the combination C(20,2) and confirming that each unordered pair yields one segment.
This easy difficulty mathematics question is from the chapter permutations and combinations, covering the topic of selection of consecutive objects. It appeared in the 2025 exam.
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