IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 24 : There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is

1. 10
2. 25
3. 35
4. 36

Video Explanation

Explanatory Answer

For making a line we need two points. And three points which are collinear will make one line only.
So in the given arrangement where we have 5 collinear points will make exactly one line.
The number of lines that can be formed among the 5 points among which no three are collinear is ⁵C₂ = 10 lines.




The number of lines that can be formed among the 5 points that are collinear is 1 as any combination of lines produces the same line.

Finally Choosing one point each from the two groups we can form 5 * 5 lines
= 25 lines



So the total number of lines is = 25 + 10 + 1 = 36 lines

The answer is '36'

Choice D is the correct answer.

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