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For a positive integer n if the mean of ...

For a positive integer n if the mean of the
binomial coefficients in the expansion of `(a + b)^(2n - 3)` is 16 Then n is equal to

A

4

B

5

C

7

D

9

Text Solution

Verified by Experts

The correct Answer is:
b
The binomail ceofficients in the expansion of
`(a + b)^(2n-3) are ""^(2n-3)C_(0)""^(2n-3)C_(1),...,... ""^(2n-3)C_(2n-3)`.
It is given that their mean is 16
`therefore (""^(2n-3)C_(0)+""^(2n-3)C_(1) + .........+ ""^(2n-3)C_(2n-3))/(2n-2)= 16`
`rArr 2^(2n-3) = 16 (2n -2)`
`rArr 2^(2n-8) = 11 -1`
`rArr n= 5` (By inspection)
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