If the ratio of the seventh term from the beginning of the binomial expansion 21 - 3-1-31 - 3x to the seventh term from the end is 1-6- then the value of X isA- 7B- 5C- 11D- 9

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General Term of Binomial Expansion

If the ratio ...

Question

If the ratio of the seventh term from the beginning of the binomial expansion of ${(2^{1 / 3} + \frac{1}{3^{1 / 3}})}^{x}$ to the seventh term from the end is $\frac{1}{6}$ , then the value of $x$ is

7

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5

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11

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9

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Solution

The correct option is D $9$
Seventh term from the beginning
$=^{x} C_{6} (2^{1 / 3})^{x - 6} (3^{- 1 / 3})^{6}$
Seventh term from the last
$=^{x} C_{x - 6} (2^{1 / 3})^{6} (3^{- 1 / 3})^{x - 6}$
We know that,
$\frac{^{x} C_{6} (2^{1 / 3})^{x - 6} (3^{- 1 / 3})^{6}}{^{x} C_{x - 6} (2^{1 / 3})^{6} (3^{- 1 / 3})^{x - 6}} = \frac{1}{6}$
$\Rightarrow x = 9$

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If the ratio of the seventh term from the beginning of the binomial expansion of (21/3+131/3)x to the seventh term from the end is 16, then the value of x is

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