The coefficient of x4 in the expansion of  1+x+x2+x311 is 

The coefficient of x4 in the expansion of  1+x+x2+x311 is 

  1. A

    900

  2. B

    909

  3. C

    990

  4. D

    999

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    Solution:

    Let E=1+x+x2+x311

    =(1+x)1+x211=(1+x)111+x211

    General term of E is,

    T(r,k)= 11Crxr 11Ckx2k

    =11Cr11Ckxr+2k  

    For taking coefficient of x4 take
    r+2k=4 

    r012345
    k=4r22x1x0x

    . Coefficient of x4  

    =T(0,2)+T(2,1)+T(4,0)=11C011C2+11C211C1+11C411C0=55+55×11+330=55+605+330=990

     

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