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Match the statements in Column-I with the given in Column-II.
Column-I Column-II
A) There are 12 points in a plane out of which 5 are collinear and no 3 of the remaining are collinear. Then the no. of lines that can be formed by joining pairs of these points is
p) 1296
B) The no. of triangles that can be formed by using the points contained above is
q) 57
C) The no. of rectangles that can be formed by Using the squares on a chess board is
r) 420
D) If a set of 8 parallel lines are intersected by Another set of 6
s) 210

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$A - r, B - p, C - q, D - s$

$A - q, B - s, C - p, D - r$

$A - s, B - p, C - q, D - r$

$A - s, B - q, C - p, D - r$

answer is A.

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Detailed Solution

A) The five collinear points gives us one straight line
The required no. is
${}^{12}C_{2} - {}^{5}C_{2} + 1 = \frac{12.11}{2} - \frac{5.4}{2} + 1 = 57$
B) A triangle is formed with 3 non-collinear points
The no. of triangle that can be formed is ${}^{12}C_{3} - {}^{5}C_{3} = 210$
C) A chess board consists of a horizontal and a vertical lines. To form a rectangle (it may be a square) we need 2 horizontal and 2 vertical lines.
The no. of rectangle is
D) We select 2 from 8 lines set and 2 from 6-lines set the number of parallelograms is.

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