JEE MAIN Linear Programming Previous Year Questions (PYQs) – Page 2 of 2
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If the system of equations
$
\begin{aligned}
2x + 3y - z &= 5, \\
x + \alpha y + 3z &= -4, \\
3x - y + \beta z &= 7
\end{aligned}
$
has infinitely many solutions, then $13\alpha\beta$ is equal to:
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Solution
Let $\lambda \in $ R . The system of linear equations
2x1- 4x2 + $\lambda $x3 = 1
x1 - 6x2 + x3 = 2
$\lambda $x1 - 10x2 + 4x3 = 3
is inconsistent for:
2x1- 4x2 + $\lambda $x3 = 1
x1 - 6x2 + x3 = 2
$\lambda $x1 - 10x2 + 4x3 = 3
is inconsistent for:
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Solution
Let $\lambda $ be a real number for which the system of linear equations x + y + z = 6, 4x + $\lambda $y – $\lambda $z = $\lambda $ – 2,
3x + 2y – 4z = – 5 has infinitely many solutions. Then $\lambda $ is a root of the quadratic equation
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Solution
If the system of linear equations
$8x + y + 4z = -2$
$x + y + z = 0$
$\lambda x - 3y = \mu$
has infinitely many solutions, then the distance of the point $(\lambda, \mu, -\tfrac{1}{2})$ from the plane $8x + y + 4z + 2 = 0$ is :
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Solution
Let $S$ denote the set of all real values of $\lambda$ such that the system of equations
$\lambda x + y + z = 1$
$x + \lambda y + z = 1$
$x + y + \lambda z = 1$
is inconsistent, then $\displaystyle \sum_{\lambda \in S}\big(|\lambda|^{2}+|\lambda|\big)$ is equal to:
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Solution
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