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Q.

The sum ∑0≤i≤j≤10 10Cj jCi is equal to

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a

210 - 1

b

210

c

310

d

310 - 1

answer is C.

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Detailed Solution

∑0≤i≤j≤10 10Cj jCi =10C00C0+10C1 1C0+1C1+10C2 2C0+2C1+2C2+…+10C10 10C0+10C1+…+10C10 =10C0+10C1(2)+10C222+10C323+…+10C10210 =(1+2)10 =310

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The sum ∑0≤i≤j≤10 10Cj jCi is equal to