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

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

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

a

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

b

\(\text { System has no solution for } \alpha=3, \beta=4 \text {. }\)

c

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

d

\(\text { System has infinitely many solutions for } \alpha=3, \beta=14 \text {. }\)

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