There are 3 set of parallel lines containing respectively p lines, q lines and r lines respectively. The greatest number of parallelograms that can be formed by the system
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a
pqr+(p−1)(q−1)(r−1)
b
14{pqr+(p−1)(q−1)(r−1)}
c
14pqr(p+1)(q+1)(r+1)
d
none of these
answer is D.
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Detailed Solution
Number of parallelograms= pC2 qC2+ qC2 rC2+ rC2 pC2
There are 3 set of parallel lines containing respectively p lines, q lines and r lines respectively. The greatest number of parallelograms that can be formed by the system