The coefficient of $x^{103}$ in $(1 + x + x^{2} + x^{3} + x^{4})^{199} . (x - 1)^{201}$ is

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Solution

The correct option is C
0

$[(x - 1) (x^{4} + x^{3} + x^{2} + x + 1)]^{199} (x - 1)^{2}$

= $(x^{5} - 1)^{199} (x^{2} - 2 x + 1)$

Coefficient of $x^{103}$ is 0 $[∴ (x^{5} - 1)^{199}$ will have all powers of x as multiples of 5 only $]$

Suggest Corrections

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