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Question:

The positive value of λ for which the coefficient of x² in the expression x²(√x + λx²)¹⁰ is 720, is:

3

4

√5

2√2

Solution:

x2(√x+λx2)10the general term=x2(10Cr(√x)10−r(λx2)2)=x2[10Cr(x)10−r2(λ)r(x)𕒶r]=[10Crλrx10𕒷r2]for the coefficient ofx2is10𕒷r2=2∴r=2Hence,10C2λ2=720λ2=16λ=±4