The ordered pair $(a, b)$, for which the system of linear equations  $3 x-2 y+z=b$  ;  $5 x-8 y+9 z=3$  ;  $2 x+y+a z=-1$ has no solution, is

  • [JEE MAIN 2022]
  • A

    $\left(3, \frac{1}{3}\right)$

  • B

    $\left(-3, \frac{1}{3}\right)$

  • C

    $\left(-3,-\frac{1}{3}\right)$

  • D

    $\left(3,-\frac{1}{3}\right)$

Similar Questions

The value of $\left| {\begin{array}{*{20}{c}}
1&x&y\\
2&{\sin x + 2x}&{\sin y + 2y}\\
3&{\cos x + 3x}&{\cos y + 3y}
\end{array}} \right|$ is

Let $A =$ $\left[ {\begin{array}{*{20}{c}}{1 + {x^2} - {y^2} - {z^2}}&{2(xy + z)}&{2(zx - y)}\\{2(xy - z)}&{1 + {y^2} - {z^2} - {x^2}}&{2(yz + x)}\\{2(zx + y)}&{2(yz - x)}&{1 + {z^2} - {x^2} - {y^2}}\end{array}} \right]$  then det. $A$ is equal to

If $\omega $ be a complex cube root of unity, then $\left| {\,\begin{array}{*{20}{c}}1&\omega &{ - {\omega ^2}/2}\\1&1&1\\1&{ - 1}&0\end{array}\,} \right| = $

The values of the determinant $\left| {\,\begin{array}{*{20}{c}}1&{\cos (\alpha - \beta )}&{\cos \alpha }\\{\cos (\alpha - \beta )}&1&{\cos \beta }\\{\cos \alpha }&{\cos \beta }&1\end{array}\,} \right|$ is

If the system of linear equations  $2 x + y - z =7$ ; $x-3 y+2 z=1$  ; $x +4 y +\delta z = k$, where $\delta, k \in R$  has infinitely many solutions, then $\delta+ k$ is equal to

  • [JEE MAIN 2022]