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Maths-

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Easy

Question

The coefficient of $x to the power of 49 end exponent$ in the product $open parentheses x minus 1 close parentheses open parentheses x minus 3 close parentheses midline horizontal ellipsis left parenthesis x minus 99 right parenthesis$ is

$- 99^{2}$
1
$- 2500$
None of these

The correct answer is: $negative 2500$

Here, number of factors is 50. Therefore, the coefficient of $x to the power of 49 end exponent$ is
$negative 1 minus 3 minus 5 minus horizontal ellipsis minus 99 equals negative fraction numerator 50 over denominator 2 end fraction open parentheses 1 plus 99 close parentheses equals negative 2500$

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