JEE Main 2024 — Determinants Question with Solution
JEE Main 2024 (05 Apr Shift 1)
Question
If the system of equations
$\begin{array}{r}
11 x+y+\lambda z=-5 \\
2 x+3 y+5 z=3 \\
8 x-19 y-39 z=\mu
\end{array}$
has infinitely many solutions, then is equal to :
Choose an option
Show full solutionCorrect option: C
Correct answer
C47
Step-by-step explanation
$\begin{aligned}
& 11 x+y+\lambda z=-5 \\
& 2 x+3 y+5 z=3 \\
& 8 x-19 y-39 z=\mu
\end{aligned}$
for infinite sol.
$\begin{aligned}
& \mathrm{D}=\left|\begin{array}{ccc}
11 & 1 & \lambda \\
2 & 3 & 5 \\
8 & -19 & -39
\end{array}\right|=0 \\
& \Rightarrow 11(-117+95)-1(-78-40)+\lambda(-38-24) \\
& \Rightarrow 11(-22)+118-\lambda(62)=0 \\
& \Rightarrow 62 \lambda=118-242 \\
& \Rightarrow \lambda=\frac{-124}{62}=-2
\end{aligned}$
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Determinants chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2024, covering the Determinants chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.