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Question

The number of the rectangles excluding squares that can be formed from a rectangle of size 9×6 if it is divided by set of parallel lines of unit length as shown in the diagram is

A
391
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B
791
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C
842
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D
None of these
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Solution

The correct option is D 791
Here, l=9 and b=6
Number of rectangles that can be selected without any restrictions is =7C2×10C2
Now the squares can be selected of dimensions r×r
(where r{1,2,...,6})
Now square of dimension 1×1 can be selected in 9×6 ways.
Similarly, square of dimension 2×2 can be selected in 8×5 ways.
Similarly, square of dimension 6×6 can be selected in 4×1 ways.
So the number of squares will be
6r=1(10r)(7r)
Number of required ways =7C2×10C26r=1(10r)(7r)
=9456r=1(7017r+r2)
=945(70×617×21+91)=791

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