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Q.

For natural numbers m,n if (1-y)m(1+y)n=1+a1y+a2y2+…, and a1=a2=10 , then (m,n) is

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a

(45,35)

b

(35,45)

c

(20,45)

d

(35,20)

answer is B.

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Detailed Solution

(1-y)m(1+y)n=1+a1y+a2y2+…⇒1-C1   my+C2   my2-…1+C1   ny+C2   ny2+…==1+a1y+a2y2+…⇒a1=C1   n-C1   m,a2=C2   mC  m1nC1nC2⇒n-m=10, m2+n2-m-n-2mn=20⇒n-m=10,( m-n)2-(m+n)=20⇒n-m=10,n+m=80⇒m=35,n=45
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