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Maths-

General

Easy

Question

The coefficient of $x to the power of 5 end exponent$ in the expansion of $open parentheses 1 plus x to the power of 2 end exponent close parentheses to the power of 5 end exponent open parentheses 1 plus x close parentheses to the power of 4 end exponent$ is

30
60
40
None of these

The correct answer is: 60

We have, $open parentheses 1 plus x to the power of 2 end exponent close parentheses to the power of 5 end exponent open parentheses 1 plus x close parentheses to the power of 4 end exponent$
$equals open parentheses blank to the power of 5 end exponent C subscript 0 end subscript plus blank to the power of 5 end exponent C subscript 1 end subscript x to the power of 2 end exponent plus blank to the power of 5 end exponent C subscript 2 end subscript x to the power of 4 end exponent plus... close parentheses left parenthesis blank to the power of 4 end exponent C subscript 0 end subscript plus blank to the power of 4 end exponent C subscript 1 end subscript x plus blank to the power of 4 end exponent C subscript 2 end subscript x to the power of 2 end exponent plus blank to the power of 4 end exponent C subscript 3 end subscript x to the power of 3 end exponent plus blank to the power of 4 end exponent C subscript 4 end subscript x to the power of 4 end exponent right parenthesis$
The coefficient of $x to the power of 5 end exponent$ in $left square bracket open parentheses 1 plus x to the power of 2 end exponent close parentheses to the power of 5 end exponent open parentheses 1 plus x close parentheses to the power of 4 end exponent right square bracket$
$equals blank to the power of 5 end exponent C subscript 2 end subscript. blank to the power of 4 end exponent C subscript 1 end subscript plus blank to the power of 4 end exponent C subscript 3 end subscript. blank to the power of 5 end exponent C subscript 1 end subscript equals 10.4 plus 4.5 equals 60$

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