First slide

Binomial theorem for positive integral Index

Question

For a positive integer $n$ if the mean of the binomial coefficients in the expansion of $(a + b)^{2 n - 3}$ is 16, then $n$ is equal to :

Moderate

A

5
B

7
C

9
D

4

Solution

Mean of binomial coefficients in the expansion of
$(a + b)^{2 n - 3}$ is
$\begin{array}{l} \frac{1}{2 n - 3 + 1} [^{2 n - 3} C_{0} +^{2 n - 3} C_{1} + \dots +^{2 n - 3} C_{2 n - 3}] \\ = \frac{1}{2 (n - 1)} 2^{2 n - 3} = \frac{2^{2 (n - 2)}}{n - 1} = 16 = 2^{4} \\ \Rightarrow n = 5 \end{array}$

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