CUET Mathematics 2025 14 May Shift 1 PYQs

If the system of equations $kx+y+z=0$, $x+ky-z=0$, $x+y+z=0$ has a non-zero solution, then the possible values of k are

If $x, y$ and $z$ are non-zero distinct numbers, then $\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}$ is equal to

For what value of k, the following system of equations has infinitely many solutions?

$x + 2y = 5, 3x + ky = 15$