The sum of the coefficients of all the even powers of x in the expansion of ${(2 x^{2} - 3 x + 1)}^{11}$ is

2 . 6^{10}

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3 . 6^{10}

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6^{11}

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None of the above

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Solution

The correct option is B $3 . 6^{10}$
Given equation is $(2 x^{2} - 3 x + 1)^{11}$
$= (2 x - 1)^{11} (x - 1)^{11}$
$= (3)^{11} . (2)^{11 - 1}$
$= 3^{11} {.2}^{10}$
$= 6^{10} .3$

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