[JEE Advanced 2005] a 2m 1 2n 1 rectangle is split into unit squares the number of
A $(2m-1)\times(2n-1)$ rectangle is split into unit squares. The number of rectangles having both sides of odd length is
(a) $(m+n-1)^2$
(b) $4^{m+n-1}$
(c) $m^2n^2$
(d) $m(m+1)n(n+1)$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (c) $m^2n^2$
Odd width: choose two of the $2m$ vertical lines an odd distance apart $=m\cdot m$; similarly $n\cdot n$ horizontally. Total $m^2n^2$.
JEE Advanced 2005 · Permutations and Combinations — verified solution by the Vidaara Team.
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