The sum of the coefficients of even powers of x in the expansion of ${(1 + x + x^{2} + x^{3})}^{5}$ is

510

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512

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521

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522

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Solution

The correct option is B 512
$Sum of the coefficients of even powers of x in f(x) is \frac{f (1) + f (- 1)}{2} = \frac{(1 + 1 + 1 + 1)^{5} + (1 - 1 - 1 - 1)^{5}}{2} = \frac{4^{5}}{2} = 512$

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