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Q.

In the expansion of x2+1+1x2n,n∈N,

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a

number of terms is 2n + 1

b

constant term is 2n-1

c

coefficient of x2n-2 is n

d

coefficient of x2 in n

answer is A.

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Detailed Solution

x2+1+1x2=nC0+nC1x2+1x2+nC2x2+1x22+⋯+nCnx2+1x2nThis contains terms having x0,x2,x4,…x2n,x−2,x−4,…,x−2ncoefficient of constant term=nC0+ nC2(2)+ nC4 4C2+ nC6 6C3+⋯≠2n−1.coefficient of x2n−2 is nCn−1=ncoefficient of x2 is nC1+ nC3 3C1+ nC5 5C2+⋯>n
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