Q. A rectangle with sides $2m - 1\$and $2n - 1$ divided into squere of unit length. The number of rectangle which can be formed with sides of odd length is
A) $m^{2}n^{2}$
B) $mn(m + 1)(n + 1)$
C) $4^{m + n - 1}$
D) None of these
Explanation
(a)
For length, number of choices is
$(2m - 1) + 2m - 3) + ... + 3 + 1 = m^{2}$
Similarly, for breadth number of choices is
$(2n - 1) + (2n - 3) + ... + 3 + 1 = n^{2}$
Hence, required number of choices is $m^{2}n^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.