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If m parallel lines in a plane are inter...

If m parallel lines in a plane are intersected by a family of n parallel lines, then the number of parallelograms that can be formed is

A

`m^n`

B

(m+1)(n+1)

C

`(m-n)/n!`

D

`mn(n-1)(n-1)/4`

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Verified by Experts

The correct Answer is:
D
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If m parallel lines in a plane are intersected by a family of n parallel lines,the number of parallelograms that can be formed is a.(1)/(4)mn(m-1)(n-1) b.(1)/(4)mn(m-1)(n-1) c.(1)/(4)m^(2)n^(2) d.none of these

Assertion: If m parallel lines are intersected by n other parallel llines, then the number of parallelograms thus formes is (mn(m-1)(n-1))/4 , Reason: A selection of 4 lines 2 form m parallel lines and 2 from n parallel lines givers one parallelogram. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

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