The sum of the coefficients of all odd exponets of $x$ in the product of $(1 - x + x^{2} - x^{3} + x^{4} + . . . - x^{49} + x^{50}) \times (1 + x + x^{2} + x^{3} + . . . + x^{50})$ equals

1

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0

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- 1

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None of these

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Solution

The correct option is B $0$
Coefficient of $x^{1}$ will be
$1 + (- 1)$
$= 0$ ..(i)
Coefficient of $x^{3}$ will be
$1 + (- 1) + 1 + (- 1)$
$= 0$
Hence the coefficients of $x^{n}$ where n is odd is zero.

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