The sum of the coefficients in the expansion of $(1 + 2 x + 5 x^{2})^{n}$ and $(1 + 3 x)^{3 n}$ are $a$ and $b$ respectively. Then

a < b

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a = b

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b = a^{3}

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b^{2} = a

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Solution

The correct option is A $a < b$
$(1 + 2 x + 5 x^{2})^{n}$
For sum of the coefficients of $x$ , we substitute $x = 1$ .
Hence sum of the coefficients of $x$ is equal to $8^{n}$
Hence $a = 8^{n}$
$(1 + 3 x)^{3 n}$
For sum of the coefficients of $x$ , we substitute $x = 1$ .
Hence sum of the coefficients of $x$ is equal to $4^{3 n}$
Hence $b = 4^{3 n}$
$= 64^{n}$
Hence $b > a$ .
The other options are not satisfied.

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