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Sum of Coefficients of All Terms

The value of ...

Question

The value of $^{10} C_{1} +^{10} C_{3} +^{10} C_{5} +^{10} C_{7} +^{10} C_{9}$ is

A

2^{7}

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B

2^{8}

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C

2^{9}

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D

2^{10}

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Solution

The correct option is C $2^{9}$
We know that
$^{n} C_{1} +^{n} C_{3} +^{n} C_{5} + \dots = 2^{n - 1}$
So,
$^{10} C_{1} +^{10} C_{3} +^{10} C_{5} +^{10} C_{7} +^{10} C_{9} = 2^{10 - 1} = 2^{9}$

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^{10} C_{1} +^{10} C_{3} +^{10} C_{5} +^{10} C_{7} +^{10} C_{9} =

^{10} C_{1} +^{10} C_{3} +^{10} C_{5} +^{10} C_{7} +^{10} C_{9} =

^{10} C_{1} +^{10} C_{3} +^{10} C_{5} +^{10} C_{7} +^{10} C_{9} =

^{10} C_{1} +^{10} C_{3} +^{10} C_{5} +^{10} C_{7} +^{10} C_{9} =

$^{10} C_{1}$ + $^{10} C_{3}$ + $^{10} C_{5}$ + $^{10} C_{7}$ + $^{10} C_{9}$ =

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Sum of Coefficients of All Terms

Standard XII Mathematics

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