Maximum sum of the coefficients in the expansion of $(1 - x sin θ + x^{2})^{n}$ is

1

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2^{n}

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3^{n}

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0

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Solution

The correct option is C $3^{n}$
${(1 - x sin θ + x^{2})}^{n}$
We can get the sum of the coefficient by directly taking $x = 1$ in the above expression.
$\Rightarrow S = {(1 - sin θ + 1)}^{n}$
$= {(2 - sin θ)}^{n}$
$- 1 \leq sin θ \leq 1$
$\Rightarrow$ Minimum value of $sin θ = - 1$
$∴$ $S_{m a x} = {(2 - (- 1))}^{n}$
$= 3^{n} .$
Hence, the answer is $3^{n} .$

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