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If in the expansion f (1+x)^m(1-x)^n, th...

If in the expansion f `(1+x)^m(1-x)^n`, the coefficient of `x` and `x^(2)` are 3 and -6 respectively then

A

6

B

9

C

12

D

24

Text Solution

Verified by Experts

The correct Answer is:
C
`(1+x)^m(1-x)^n=[1+mx+(m(m-1))/(2)x^2+......]`
`[1-nx+(n(n-1))/(2)x^2+.......]`
`=1+(m-n)x+[(m(m-1))/(2)+(n(n-1))/(2)-mn]x^2+......`
term containg power of `x ge 3`.
Now `m-n=3 .....(i)`
and `(1)/(2)m(m-1)+(1)/(2)n(n-1)-mn=-6`.
`rArr m(m-1)+nn(n-1)-2mn=-12`.
`rArr m^2-m+n^2-n-2mn=-12`
`rArr (m-n)^2-(m+n)=-12`
`rArr m=n=9+12=21....(ii)`.
On solving Eqs.(i) and (ii), we get `m=12`.
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