First slide

Binomial theorem for positive integral Index

Question

The last term in the binomial expansion of ${(\sqrt{2} - \frac{1}{\sqrt{2}})}^{n}$ is ${(\frac{1}{(3) 9^{\frac{1}{3}}})}^{\log 3}$ then the 5th term from the beginning is

Moderate

A

$^{10} C_{6}$
B

$2 (^{10} C_{4})$
C

$\frac{1}{2} (^{10} C_{4})$
D

$-^{10} C_{6}$

Solution

$^{n} C_{n} {(- \frac{1}{\sqrt{2}})}^{n} = {(3^{- 1 - 2 / 3})}^{\log_{3}^{8}} = 3^{- 5 \log_{3}^{2}} = \frac{1}{2^{5}}$
$\Rightarrow n = 10$
$∴$ 5th term from the beginning
$=^{10} C_{4} (\sqrt{2})^{10 - 4} {(- \frac{1}{\sqrt{2}})}^{4} = 2 (^{10} C_{4})$

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