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If ${(3 x - 1)}^{7} = a_{7} x^{7} + a_{6} x^{6} + a_{5} x^{5} + .... + a_{1} x + a_{0},$ then $a_{7} + a_{6} + a_{5} + .... + a_{1} + a_{0} =$

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128

answer is C.

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Detailed Solution

{(3 x - 1)}^{7} = a_{7} x^{7} + a_{6} x^{6} + a_{5} x^{5} + .... + a_{1} x^{1} + a_{0}

Put $x = 1$

${(3 (1) - 1)}^{7} = a_{7} + a_{6} + a_{5} + .... + a_{1} + a_{0}$

$2^{7} = a_{0} + a_{1} + a_{2} + ..... + a_{7}$

$a_{0} + a_{1} + a_{2} + ..... + a_{7} = 128$

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