3003010−3013011+…+30203030 is equal to

30030103013011++30203030 is equal to

  1. A

     30C11

  2. B

     60C10

  3. C

     30C10

  4. D

     65C55

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    Solution:

     Let A=30030103013011+3023012+30203030

     or A=30C030C1030C130C11+30C230C12+30C2030C30 

    = Coefficient of x20 in (1+x)30(1x)30= Coefficient of x20 in 1x230= Coefficient of x20 in r=030(1)r30Crx2r=(1)10  30C10  [for coefficient of x20, let r=10=30C10

    =(1)10  30C10  [for coefficient of x20, let r=10=30C10

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