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Q.

∑ ∑0≤i≤j≤10 10Cj jCi is equal to

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a

310

b

310 – 1

c

210

d

210 – 1

answer is A.

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Detailed Solution

∑ ∑0≤i≤j≤10 10Cj jCi=10C0×0C0+10C1 1C0+1C1+10C2 2C0+2C1+2C2+10C3 3C0+3C1+3C2+3C3+…+10C10 10C0+10C1+…+10C10 =10C0⋅20+10C1⋅21+10C2⋅22+…+10C10⋅210 =(1+2)10=310

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∑ ∑0≤i≤j≤10 10Cj jCi is equal to