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Q.

If in the expansion of (1+x)m(1-x)n coefficient of x and x2 and 7 and 18 respectively, then (m,n)  is equal to

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a

(3,8)

b

(8,4)

c

(10,3)

d

(11,4)

answer is C.

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Detailed Solution

(1+x)m(1-x)n=1+C1   mx+C2   mx2+….1-C1   nx+C2   nx2-….=1+C1   m-C1   nx+C2   m+C2   n-C1   mC1   nx2+…=1+(m-n)x+12m(m-1)+n(n-1)-2(m+n)=36]We have m-n=7 and 12nn-1+mm-1-2mn =18⇒m-n=7, m2+n2-2mn-(m+n)=36⇒m-n=7,(m-n)2-(m+n)=36⇒m-n=7,m+n=13⇒m=10, n=3
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