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The sum ""^(20)C(0)+""^(20)C(1)+""^(20)C...

The sum `""^(20)C_(0)+""^(20)C_(1)+""^(20)C_(2)+……+""^(20)C_(10)` is equal to :

A

`2^26`

B

`2^23`

C

`2^24`

D

`22^25`

Text Solution

Verified by Experts

The correct Answer is:
D
`sum_(r=0)^20(3r+2)^20C_r`
`=3sum_(r=0)^20r^20Cr+2sum_(r=0)^20Cr`
`3sum_(r=0)^(20)20xx^19C_(r-1)+2xx2^20`
`3xx20(2)^19+2xx(2)^20`
`2^21(15+1)=2^25`
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