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if in the expansion of (1+x)^m (1-x)^n t...

if in the expansion of `(1+x)^m (1-x)^n` the cofficients of x and` x^2` are 3 and -6 respectively then m is

A

6

B

9

C

12

D

24

Text Solution

Verified by Experts

`(1+x)^m(1-x)^n=[1+mx+((m)(m-1).x^2)/(2)+...][1-nx+(n(n-1))/(2)x^2+....]`
Coefficient of x=m-n =3
Coefficient of `x^2=-mn+(n(n+1))/(2)+(m(m-1))/(2)=-6 `
Solving (i) and (ii) ,we get
m=12 and n=9
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