10 C 1-10 C 3-10 C 5-10 C 7-10 C 9-A- 210B- 29C- 210-1D- None of these

The correct option is B 29We know that 2^n 1=^nC_0+^nC_2+^nC_4+.....=^nC_1+^nC_3+^nC_5+....... So, ^10C_1+^10C_3+^10C_5+......+^10C_9= 2^10 1= 2^9 ...

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Byju's Answer

Standard XI

Mathematics

Sum of binomial coefficients with alternate signs

10 C 1+10 C 3...

Question

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

2⁹

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2¹⁰

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2¹⁰-1

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None of these

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Solution

The correct option is A 2⁹
We know that
$2^{n - 1} =^{n} C_{0} +^{n} C_{2} +^{n} C_{4} + . . . . . =^{n} C_{1} +^{n} C_{3} +^{n} C_{5} + . . . . . . .$
So, $^{10} C_{1} +^{10} C_{3} +^{10} C_{5} + . . . . . . +^{10} C_{9} = 2^{10 - 1} = 2^{9}$

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Similar questions

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

^{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} =

Q. The value of

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

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10C1+10C3+10C5+10C7+10C9=

The correct option is A 29We know that 2n−1=nC0+nC2+nC4+.....=nC1+nC3+nC5+....... So, 10C1+10C3+10C5+......+10C9=210−1=29

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

The correct option is A 2⁹
We know that
$2^{n - 1} =^{n} C_{0} +^{n} C_{2} +^{n} C_{4} + . . . . . =^{n} C_{1} +^{n} C_{3} +^{n} C_{5} + . . . . . . .$
So, $^{10} C_{1} +^{10} C_{3} +^{10} C_{5} + . . . . . . +^{10} C_{9} = 2^{10 - 1} = 2^{9}$