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Maths-

General

Easy

Question

The value of $open parentheses blank to the power of 21 end exponent C subscript 1 end subscript minus blank to the power of 10 end exponent C subscript 1 end subscript close parentheses plus open parentheses blank to the power of 21 end exponent C subscript 2 end subscript minus blank to the power of 10 end exponent C subscript 2 end subscript close parentheses plus open parentheses blank to the power of 21 end exponent C subscript 3 end subscript minus blank to the power of 10 end exponent C subscript 3 end subscript close parentheses plus open parentheses blank to the power of 21 end exponent C subscript 4 end subscript minus blank to the power of 10 end exponent C subscript 4 end subscript close parentheses plus midline horizontal ellipsis plus open parentheses blank to the power of 21 end exponent C subscript 10 end subscript minus blank to the power of 10 end exponent C subscript 10 end subscript close parentheses text end text$ is

$2^{21} - 2^{10}$
$2^{20} - 2^{9}$
$2^{20} - 2^{10}$
$2^{21} - 2^{11}$

The correct answer is: $2 to the power of 20 end exponent minus 2 to the power of 10 end exponent$

$open blank to the power of 21 end exponent C subscript 1 end subscript plus blank to the power of 21 end exponent C subscript 2 end subscript plus midline horizontal ellipsis plus blank to the power of 21 end exponent C subscript 10 end subscript close parentheses minus open parentheses blank to the power of 10 end exponent C subscript 1 end subscript plus blank to the power of 10 end exponent C subscript 2 end subscript plus midline horizontal ellipsis plus blank to the power of 10 end exponent C subscript 10 end subscript close parentheses$
$table row cell equals fraction numerator 1 over denominator 2 end fraction open square brackets 2 cross times blank to the power of 21 end exponent C subscript 1 end subscript plus 2 x blank to the power of 21 end exponent C subscript 2 end subscript plus midline horizontal ellipsis plus 2 x blank to the power of 21 end exponent C subscript 10 end subscript close square brackets minus open parentheses 2 to the power of 10 end exponent minus 1 close parentheses end cell row cell equals fraction numerator 1 over denominator 2 end fraction open parentheses blank to the power of 21 end exponent C subscript 0 end subscript plus blank to the power of 21 end exponent C subscript 1 end subscript plus blank to the power of 21 end exponent C subscript 2 end subscript plus midline horizontal ellipsis plus blank to the power of 21 end exponent C subscript 10 end subscript plus blank to the power of 21 end exponent C subscript 11 end subscript plus midline horizontal ellipsis plus blank to the power of 21 end exponent C subscript 20 end subscript plus blank to the power of 21 end exponent C subscript 21 end subscript close end cell end table$
$open negative open parentheses blank to the power of 21 end exponent C subscript 0 end subscript plus blank to the power of 21 end exponent C subscript 21 end subscript close parentheses close square brackets minus open parentheses 2 to the power of 10 end exponent minus 1 close parentheses$
$table row cell equals fraction numerator 1 over denominator 2 end fraction open parentheses 2 to the power of 21 end exponent minus 2 close parentheses minus open parentheses 2 to the power of 10 end exponent minus 1 close parentheses end cell row cell equals 2 to the power of 20 end exponent minus 1 minus 2 to the power of 10 end exponent plus 1 end cell row cell equals 2 to the power of 20 end exponent minus 2 to the power of 10 end exponent end cell end table$

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