If the system of equations

$ 2 x+7 y+\lambda z=3 $

$ 3 x+2 y+5 z=4 $

$ x+\mu y+32 z=-1$

has infinitely many solutions, then $(\lambda-\mu)$ is equal to $\qquad$

  • [JEE MAIN 2024]
  • A

    $38$

  • B

    $39$

  • C

    $34$

  • D

    $15$

Similar Questions

$\left| {\,\begin{array}{*{20}{c}}{{{({a^x} + {a^{ - x}})}^2}}&{{{({a^x} - {a^{ - x}})}^2}}&1\\{{{({b^x} + {b^{ - x}})}^2}}&{{{({b^x} - {b^{ - x}})}^2}}&1\\{{{({c^x} + {c^{ - x}})}^2}}&{{{({c^x} - {c^{ - x}})}^2}}&1\end{array}\,} \right| = $

If $|A|$  denotes the value of the determinant of the square matrix $A$ of order $3$ , then $ |-2A|=$

For how many diff erent values of $a$ does the following system have at least two distinct solutions?

$a x+y=0$

$x+(a+10) y=0$

  • [KVPY 2017]

 If the system of equations $2 x-y+z=4$, $5 x+\lambda y+3 z=12$,$100 x-47 y+\mu z=212$ has infinitely many solutions, then $\mu-2 \lambda$ is equal to

  • [JEE MAIN 2025]

For the system of linear equations

$2 x-y+3 z=5$

$3 x+2 y-z=7$

$4 x+5 y+\alpha z=\beta$

Which of the following is NOT correct ?

  • [JEE MAIN 2023]