If for positive integers $r> 1, n > 2$, the coefficients of the $(3r)^{th}$ and $(r + 2)^{th}$ powers of $x$ in the expansion of $( 1 + x)^{2n}$ are equal, then $n$ is equal to 

  • [JEE MAIN 2013]
  • A

    $2r+ 1$

  • B

    $2r- 1$

  • C

    $3r$

  • D

    $r+1$

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  • [JEE MAIN 2023]