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Questions  

In the expansion of (1+px)n,nN, the coefficient of x and x2 are 8 and 24 respectively, then

a
n=3, p=2
b
n=4, p=2
c
n=4, p=3
d
n=5, p=3

detailed solution

Correct option is B

We have (1+px)n=1+nC1(px)+nC2(px)2+…=1+npx+12n(n−1)p2x2+…According to the hypothesis,               np=8 and 12n(n−1)p2=24Putting p=8/n in the second expression, we get12n(n−1)8n2=24⇒n−1n=24×28×8=34⇒4n−4=3n⇒n=4Putting this value in np=8, we get p=2.

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