Let $N$ denote the number that turns up when a fair die is rolled. If the probability that the system of equations

$x+y+z=1$  ;  $2 x+N y+2 z=2$  ;  $3 x+3 y+N z=3$

has unique solution is $\frac{k}{6}$, then the sum of value of $k$ and all possible values of $N$ is

  • [JEE MAIN 2023]
  • A

    $18$

  • B

    $19$

  • C

    $20$

  • D

    $21$

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