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Question

The value of r for which 20Cr 20C0+ 20Cr1 20C1+ 20Cr2 20C2++ 20C0 20Cr is maximum, is :

A
11
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B
15
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C
10
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D
20
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Solution

The correct option is D 20
Let S= 20Cr 20C0+ 20Cr1 20C1+ 20Cr2 20C2++ 20C0 20Cr
The sum S is the coefficient of xr in the expansion of (1+x)20(x+1)20=(1+x)40
S= 40Cr
S is maximum when r=20

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