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Question

In the expansion of (1+x)m(1x)n, the coefficients of x and x2 are respectively 3 and -6.  Then m equals :


  1. 9

  2. 6

  3. 12

  4. 24


Solution

The correct option is C

12


(1+x)m(1x)n=(1+mC1x+mC2x2+..........+mCmxm)(1nC1x+nC2x2......) 

Coefficeint of x = m C1 - n C1  = 3 

m - n = 3   .........(1)

Coeffiecient of x2 = mC2+nC2mC1.nC1=6

m(m1)2+n(n1)2 - mn = -6   ........(2)

From (1) and (2)  (n+3)(n+2)2+n(n1)2n(n+3)=6 

n2+5n+6+n22n26n=12 

-2n = -18 , n = 9

m = n + 3 = 12 

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