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🛠️ JEE➗ Maths

Consider the following system of equations \(\alpha\)x + 2y + z = 1 2\(\alpha\)x + 3y + z = 1 3x + \(\alpha\)y + 2z = \(…

Q1

Consider the following system of equations

\(\alpha\)x + 2y + z = 1 2\(\alpha\)x + 3y + z = 1

3x + \(\alpha\)y + 2z = \(\beta\)

for some \(\alpha ,\beta \in R\). Then which of the following is NOT correct.

[JEE Main 2023, 29 Jan (Shift 1)]

a

It has no solution for \(\alpha\) = 3 and for all \(\beta\) ≠ 2

b

It has no solution for \(\alpha\) = –1 and for all \(\beta\)\(\in\)R.

c

It has a solution for all \(\alpha\) ≠ –1 and \(\beta\) = 2

d

It has no solution if \(\alpha\) = –1 and \(\beta\) ≠ 2

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