Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET

Previous Year Question (PYQs)



There are 15 points in a plane such that 5 points are collinear and no three of the remaining points are collinear then total number of straight lines formed are:





Solution

Solution:

Number of straight lines from \(n\) points (no three collinear) is \(\binom{n}{2}\).

Here, \(n = 15\).

\[ \binom{15}{2} = \frac{15 \times 14}{2} = 105 \]

Adjustment for collinearity:
Out of 15 points, 5 are collinear.
Lines from these 5 points = \(\binom{5}{2} = 10\).
But actually they form only 1 line.
Extra counted = \(10 - 1 = 9\).

Correct total lines:

\[ 105 - 9 = 96 \]

Final Answer: The total number of straight lines formed = 96



Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More


Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

Ask Your Question or Put Your Review.

loading...
Dhiraj-pic
Dhiraj , CUETVerified
Commented Mar 23 , 2025
15c2-5c2+1=105-10+1=96

Your reply to this comment :


loading...