If $C_r= ^{100}{C_r}$ , then $1.C^2_0 - 2.C^2_1 + 3.C^2_3 - 4.C^2_0 + 5.C^2_4 - .... + 101.C^2_{100}$ is equal to

  • A

    ${100.^{100}}{C_{50}}\,\,\,$

  • B

    ${51.^{100}}{C_{50}}\,\,\,$

  • C

    ${100.^{200}}{C_{100}}\,\,\,$

  • D

    ${51.^{200}}{C_{100}}\,\,\,$

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