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Question

A rectangle with side lengths as 2m−1 and 2n−1 units is divided into squares of unit length by drawing parallel lines as shown in diagram, then the number of rectangles possible with odd side length is

A
(m+n1)2
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B
4m+n1
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C
m2n2
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D
m(m+1)n(n+1)
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Solution

The correct option is C m2n2
Along horizontal side one unit can be taken in =(2m1) ways
3 units can be taken in =(2m3) ways
5 units can be taken in =(2m5) ways and so on

The number of ways of selecting a side horizontally is
(2m1)+(2m3)+(2m5)+...+3+1=m2

Similarly the number of ways of selecting a side vertically is
(2n1)+(2n3)+(2n5)+...+3+1=n2
total number of rectangles = m2n2

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