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Question

If A(i,j) be the coefficient of ai bj c2010−i−j in the expansion of (a+b−c)2010 then

A
Ai, i is defined for i ?1010
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B
Ai, j = Aj, i
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C
A.2i, 3i is defined for i ?405
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D
A0, 1 = 2000
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Solution

The correct option is B Ai, j = Aj, i

Clearly, Ai,j=2010!i!j!(2010ij)!
Aj,i=2010!j!i!(2010ij)!
Hence, Ai,j=Aj,i


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