JEE Main2006MathematicsBinomial TheoremActual

For natural numbers m, n if (1-y)^m(1+y)^n=1+a₁ y+a₂ y^2+ , and a₁=a₂=10 then ( m , n ) is

Options

A(20, 45)
B(35, 20)
C(45, 35)
D(35, 45)

Correct answer

D. (35, 45)

Step-by-step solution

(1-y)^m(1+y)^n= [1- ^m C₁ y+ ^m C₂ y^2- ] [1+ ^n C₁ y+ ^n C₂ y^2+ ]=1+(n-m)+ m(m-1) 2 + n(n-1) 2 -m n y^2+ . . a₁=n-m=10 and a₂= m^2+n-m-n-2 m n 2 =10 So, n-m=10 and (m-n)^2-(m+n)=20 m+n=80 m =35, n =45

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