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AIEEE 2011 Solved Paper

Section: Mathematics

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Question : 65 of 91

Marks: +1, -0

These are 10 points in a plane, out of these 6 are collinear, if

N

is the number of triangles formed by joining these points. then:

$N \leq 100$
$100 < N \leq 140$
$140 < N \leq 190$
$N > 190$

Solution:

We need 3 points to create a triangle. With 10 points number of triangle possible

{}^{10}C_3

Here 6 points are on the same line so we can't make any triangle with those 6 points.

So subtract

{}^{6}C_3

.

\therefore N={}^{10}C_3-{}^{6}C_3

=\;\frac{10.9 .8}{1.2 .3}-\;\frac{6.5 .4}{1.2 .3}

=120-20

=100

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