If the sum of the coefficients in the expansion of $(1 - 3 x + 10 x^{2})^{n}$ is $a$ and if the sum of the coefficients in the expansion of $(1 + x^{2})^{n}$ is $b$ , then

a = 3 b

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a = b^{3}

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b = a^{3}

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none of these

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Solution

The correct option is B $a = b^{3}$
Given ,
$a =$ sum of the coefficient in the expansion of $(1 - 3 x + 10 x^{2})^{n}$
$\Rightarrow a = (1 - 3 + 10)^{n} = (8)^{n}$ (Putting $x = 1$ )
$\Rightarrow a = (2)^{3 n}$
Now, $b =$ sum of the coefficients in the expansion of $(1 + x^{2})^{n}$
$\Rightarrow b = (1 + 1)^{n} = 2^{n}$ (Putting $x = 1$ )
Clearly, $a = b^{3}$

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