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Question

The interval in which x must lie so that the numerically greatest term in the expansion of (1−x)21 has the greatest coefficient is (ab,65)
Find the value of a+b

A
8
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B
9
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C
10
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D
11
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Solution

The correct option is D 11
If n is odd, then numerically greatest coefficient in the expansion of
(1x)n is nCn12 or nCn+12
Therefore in (1x)21, the numerically greatest coefficient is 21C10 or 21C11.
So, the numerically greatest term
=21C11x11 or 21C10x10 and 21C10x10>21C9.x9
21!10!11!>21!9!10!x and 21!11!10!x>21!9!12!(x>0)
x<65 and x>56x(56,65)

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