JEE Main 2025 — Determinants Question with Solution
JEE Main 2025 (24 Jan Shift 2)
Question
If the system of equations
$\begin{aligned}
& x+2 y-3 z=2 \\
& 2 x+\lambda y+5 z=5 \\
& 14 x+3 y+\mu z=33
\end{aligned}$
has infinitely many solutions, then is equal to :
Choose an option
Show full solutionCorrect option: C
Correct answer
C12
Step-by-step explanation
$\begin{aligned}
& \Delta=\left|\begin{array}{ccc}
1 & 2 & -3 \\
2 & \lambda & 5 \\
14 & 3 & \mu
\end{array}\right|=0 \Rightarrow \lambda \mu+42 \lambda-4 \mu+107=0 \\
& \Delta_1=\left|\begin{array}{ccc}
2 & 2 & -3 \\
5 & \lambda & 5 \\
33 & 3 & \mu
\end{array}\right|=0 \Rightarrow 2 \lambda \mu+99 \lambda-10 \mu+255=0 \\
& \Delta_2=\left|\begin{array}{ccc}
1 & 2 & -3 \\
2 & 5 & 5 \\
14 & 33 & \mu
\end{array}\right|=0 \Rightarrow \mu=13
\end{aligned}$
Also,
Hence,
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