Question

Assertion :The no.of parallelograms in a chess board is $1296$. Reason: The no.of parallelograms when a set of $m$ parallel lines is intersected by another set of $n$ parallel lines is ${}^m{C}_2{.}^n{C}_2$

• A. Assertion is correct and Reason is incorrect
• B. Assertion is incorrect and Reason is correct
• C. Both Assertion and Reason are correct and Reason is correct explanation of Assertion
• D. Both Assertion and Reason are correct and Reason is not correct explanation of Assertion

Answer 1

The correct option is C Both Assertion and Reason are correct and Reason is correct explanation of Assertion

Number of parallelograms from a mesh having $m$ and $n$ horizontal and vertical lines respectively is given by ${}^m{C}_2{\times }^n{C}_2$

In a chess board $m=9$ and $n=9$ so number fo parallelograms are given by ${}^9{C}_2{\times }^9{C}_2=1296$