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🛠️ JEE➗ Maths

For the system of equations \(\begin{aligned}& x+y+z=6 \\& x+2 y+\alpha z=10\\&x+3 y+5 z=\beta\end{aligned}\…

Q1

For the system of equations
\(\begin{aligned}& x+y+z=6 \\& x+2 y+\alpha z=10\\&x+3 y+5 z=\beta\end{aligned}\),
which one of the following is NOT true?

[JEE Main 2023, 6 Apr (Shift 2)]

a

System has a unique solution for \(\alpha=3, \beta \neq 14\)

b

System has no solution for \(\alpha=3, \beta=4\)

c

System has a unique solution for \(\alpha=-3, \beta=14\)

d

System has infinitely many solutions for \(\alpha=3, \beta=14\)

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