A) \[{{(m+n+1)}^{2}}\]
B) \[mn(m+1)\,(n+1)\]
C) \[{{4}^{m+n-2}}\]
D) \[{{m}^{2}}{{n}^{2}}\]
Correct Answer: D
Solution :
Along horizontal side one unit can be taken in (2m-1) ways and 3 unit side can be taken in \[2m-3\] ways. \ The number of ways of selecting a side horizontally is \[(2m-1+2m-3+2m-5+....+3+1)\] Similarly the number of ways along vertical side is\[(2n-1+2n-3+....+5+3+1)\]. \Total number of rectangles \[=[1+3+5+.....+(2m-1)]\times [1+3+5+....+(2n-1)]\] \[=\frac{m(1+2m-1)}{2}\times \frac{n(1+2n-1)}{2}={{m}^{2}}{{n}^{2}}\].You need to login to perform this action.
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