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Question

Let OA=a, OB=10a+2b and OC=b, where O,A and C are non collinear points. Let p denote the area of quadrilateral OABC, and q denote the area of the parallelogram with OA and OC as adjecent sides, then pq is equal to

A
4
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B
6
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C
12aba
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D
None of these
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Solution

The correct option is B 6
In quadrilateral OABC, adjacent sides are OA and AB, i.e. a and 9a+2b
Area of a quadrilateral is half the product of its diagonals.

So, Area =12|(ba)×(10a+2b)|

=12|10b×a+2b×a|

=6|a×b|=p

Now the area of parallelogram with adjacent sides OA,OC will be |a×b|=q
Thus the ratio between the two areas =pq=6

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