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21 Apr 2022, 02:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
44% (02:02) correct
56%
(02:04)
wrong
based on 105
sessions
History
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Not Attempted Yet
There are ten points in a plane. Of these ten points, four points are in a straight line and with the exception of these four points, no three points are in the same straight line. What is the number of straight lines formed, by joining these ten points?
A. 16
B. 24
C. 32
D. 39
E. 40
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
A. 16
B. 24
C. 32
D. 39
E. 40
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
PyjamaScientist
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21 Apr 2022, 03:59
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You need two points to make a straight line. So, \(10C2\) gives the total no. of straight lines = 45.
But we have four collinear points, so we get effectively only one straight line from those four points, so we need to subtract \(4C2\) from \(10C2\) but add 1 for four points give one line.
So, total straight lines = \(10C2 - 4C2 + 1 = 45 - 6 + 1 = 40\). (E)
But we have four collinear points, so we get effectively only one straight line from those four points, so we need to subtract \(4C2\) from \(10C2\) but add 1 for four points give one line.
So, total straight lines = \(10C2 - 4C2 + 1 = 45 - 6 + 1 = 40\). (E)
21 Apr 2022, 08:51
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To form a straight line, any 2 points have to be selected from a given set of points. Note that the order in which the points are selected does not matter here, therefore, this is a question on Combinations.
The plane contains 10 points, of which 4 are collinear. By definition, collinear points are points on the same line. Therefore, selecting any 2 points of these will not give us different straight lines. However, we cannot ignore the line on which these 4 points lie.
Therefore, total number of straight lines satisfying the above constraints = \(10_C_2\) – \(4_C_2\) + 1
\(10_C_2\) = \(\frac{{10 * 9} }{ 2}\) = 45
\(4_C_2\) = \(\frac{{4 * 3} }{ 2}\) = 6
Total number of straight lines = 45 – 6 + 1 = 40.
The correct answer option is E.
Answer option D is a very common trap answer marked by test-takers who ignore / forget the line which contains the 4 collinear points.
The plane contains 10 points, of which 4 are collinear. By definition, collinear points are points on the same line. Therefore, selecting any 2 points of these will not give us different straight lines. However, we cannot ignore the line on which these 4 points lie.
Therefore, total number of straight lines satisfying the above constraints = \(10_C_2\) – \(4_C_2\) + 1
\(10_C_2\) = \(\frac{{10 * 9} }{ 2}\) = 45
\(4_C_2\) = \(\frac{{4 * 3} }{ 2}\) = 6
Total number of straight lines = 45 – 6 + 1 = 40.
The correct answer option is E.
Answer option D is a very common trap answer marked by test-takers who ignore / forget the line which contains the 4 collinear points.
