Let for any three distinct consecutive terms $a, b, c$ of an $A.P,$ the lines $a x+b y+c=0$ be concurrent at the point $\mathrm{P}$ and $\mathrm{Q}(\alpha, \beta)$ be a point such that the system of equations $ x+y+z=6, $ $ 2 x+5 y+\alpha z=\beta$ and $x+2 y+3 z=4$, has infinitely many solutions. Then $(P Q)^2$ is equal to________.
Let for any three distinct consecutive terms $a, b, c$ of an $A.P,$ the lines $a x+b y+c=0$ be concurrent at the point $\mathrm{P}$ and $\mathrm{Q}(\alpha, \beta)$ be a point such that the system of equations $ x+y+z=6, $ $ 2 x+5 y+\alpha z=\beta$ and $x+2 y+3 z=4$, has infinitely many solutions. Then $(P Q)^2$ is equal to________.
- [JEE MAIN 2024]
- A
$123$
- B
$113$
- C
$421$
- D
$131$
Similar Questions
If $\omega $ is a cube root of unity and $\Delta = \left| {\begin{array}{*{20}{c}}1&{2\omega }\\\omega &{{\omega ^2}}\end{array}} \right|$, then ${\Delta ^2}$ is equal to
If $\omega $ is a cube root of unity and $\Delta = \left| {\begin{array}{*{20}{c}}1&{2\omega }\\\omega &{{\omega ^2}}\end{array}} \right|$, then ${\Delta ^2}$ is equal to
If $a$, $b$, $c$, $d$, $e$, $f$ are in $G.P$., then the value of $\left| {\begin{array}{*{20}{c}}
{{a^2}}&{{d^2}}&x \\
{{b^2}}&{{e^2}}&y \\
{{c^2}}&{{f^2}}&z
\end{array}} \right|$ depends on
If $a$, $b$, $c$, $d$, $e$, $f$ are in $G.P$., then the value of $\left| {\begin{array}{*{20}{c}}
{{a^2}}&{{d^2}}&x \\
{{b^2}}&{{e^2}}&y \\
{{c^2}}&{{f^2}}&z
\end{array}} \right|$ depends on
The system of equations $kx + 2y\,-z = 1$ ; $(k\,-\,1)y\,-2z = 2$ ; $(k + 2)z = 3$ has unique solution, if $k$ is equal to
The system of equations $kx + 2y\,-z = 1$ ; $(k\,-\,1)y\,-2z = 2$ ; $(k + 2)z = 3$ has unique solution, if $k$ is equal to
The system of equations $x + y + z = 6$, $x + 2y + 3z = 10,x + 2y + \lambda z = \mu $, has no solution for
The system of equations $x + y + z = 6$, $x + 2y + 3z = 10,x + 2y + \lambda z = \mu $, has no solution for