The coefficient of $x ^{301}$ in $(1+x)^{500}+x(1+x)^{499}+x^2(1+x)^{498}+\ldots . .+x^{500}$ is:

  • [JEE MAIN 2023]
  • A

    ${ }^{501} C _{302}$

  • B

    ${ }^{500} C _{301}$

  • C

    ${ }^{500} C _{300}$

  • D

    ${ }^{501} C _{200}$

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