JEE Advance - Mathematics (2005 - No. 20)
A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel lines as shown in the diagram, then the number of rectangles possible with odd side lengths is
$${(m + n - 1)^2}$$
$${4^{m + n - 1}}$$
$${m^2}\,{n^2}$$
$$m(m + 1)\,n\,(m + 1)$$