JEE MAIN Linear Programming Previous Year Questions (PYQs) – Page 1 of 2

For the system of linear equations: $x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k \in R$, consider the following statements : 

Let $\theta \in \left( {0,{\pi \over 2}} \right)$. If the system of linear equations $(1 + {\cos ^2}\theta )x + {\sin ^2}\theta y + 4\sin 3\,\theta z = 0$, ${\cos ^2}\theta x + (1 + {\sin ^2}\theta )y + 4\sin 3\,\theta z = 0$, ${\cos ^2}\theta x + {\sin ^2}\theta y + (1 + 4\sin 3\,\theta )z = 0,$ has a non-trivial solution, then the value of $\theta$ is :

Let the system of linear equations $x + y + \alpha z = 2$, $3x + y + z = 4$, $x + 2z = 1$ have a unique solution $(x^*, y^*, z^*)$. If $(\alpha, x^*)$, $(y^*, \alpha)$ and $(x^*, -y^*)$ are collinear points, then the sum of absolute values of all possible values of $\alpha$ is ?

If the system of equations $x+4y-z=\lambda,; 7x+9y+\mu z=-3,; 5x+y+2z=-1$ has infinitely many solutions, then $(2\mu+3\lambda)$ is equal to:

If the system of linear equations

$2x + 3y - z = - 2$

$x + y + z = 4$

$x - y + |\lambda |z = 4\lambda - 4$

where, $\lambda$ $\in$ R, has no solution, then

The shortest distance between the lines $\dfrac{x - 3}{4} = \dfrac{y + 7}{-11} = \dfrac{z - 1}{5}$ and $\dfrac{x - 5}{3} = \dfrac{y - 9}{-6} = \dfrac{z + 2}{1}$ is:

Let $\lambda,\mu\in\mathbb{R}$. If the system of equations $3x+5y+\lambda z=3$ $7x+11y-9z=2$ $97x+155y-189z=\mu$ has infinitely many solutions, then $\mu+2\lambda$ is equal to:

Let the line $L$ intersect the lines $x-2=-y=z-1$, $2(x+1)=2(y-1)=z+1$ and be parallel to the line $\dfrac{x-2}{3}=\dfrac{y-1}{1}=\dfrac{z-2}{2}$. Then which of the following points lies on $L$?

If the system of equations $2x+y-z=5$ $2x-5y+\lambda z=\mu$ $x+2y-5z=7$ has infinitely many solutions, then $(\lambda+\mu)^2+(\lambda-\mu)^2$ is equal to:

If the system of linear equations

$ \begin{aligned} & 3 x+y+\beta z=3 \\ & 2 x+\alpha y-z=-3 \\ & x+2 y+z=4 \end{aligned} $

has infinitely many solutions, then the value of $22 \beta-9 \alpha$ is