The system of equations  $-k x+3 y-14 z=25$  $-15 x+4 y-k z=3$  $-4 x+y+3 z=4$  is consistent for all $k$ in the set

  • [JEE MAIN 2022]
  • A

    $R$

  • B

    $R -\{-11,13\}$

  • C

    $R -\{13\}$

  • D

    $R -\{-11,11\}$

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  • [JEE MAIN 2024]

If $-9 $ is a root of the equation $\left| {\,\begin{array}{*{20}{c}}x&3&7\\2&x&2\\7&6&x\end{array}\,} \right| = 0$ then the other two roots are

  • [IIT 1983]

If the system of equations, $x + 2y - 3z = 1$, $(k + 3)z = 3,$ $(2k + 1)x + z = 0$is inconsistent, then the value of $ k$  is

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