Mathematics · 2025
JEE Main · 7 April 2025, Shift 2 · Q5
Let the system of equations x+5 y-z=1; 4 x+3 y-3 z=7; 24 x+y+λ z=μ λ, μ ∈ R, have infinitely many solutions. Then the number of the solutions of this…
Let the system of equations
$$\begin{aligned}
& x+5 y-z=1 \\
& 4 x+3 y-3 z=7 \\
& 24 x+y+\lambda z=\mu
\end{aligned}
$$
$\displaystyle \lambda, \mu \in \mathbf{R}$, have infinitely many solutions. Then the number of the solutions of this system, if $\displaystyle x, y, z$ are integers and satisfy $\displaystyle 7 \leqslant x+y+z \leqslant 77$, is :
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 3$
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JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.