If $\left|\begin{array}{ll}2017 & 2018 \\ 2019 & 2020\end{array}\right|+\left|\begin{array}{ll}2021 & 2022 \\ 2023 & 2024\end{array}\right|=2 k$,then $k^3=$ . . . . . .

The values of $\theta, \lambda$ for which the following equations $\sin \theta x - \cos \theta y + (\lambda + 1)z = 0$; $\cos \theta x + \sin \theta y - \lambda z = 0$; $\lambda x + (\lambda + 1)y + \cos \theta z = 0$ have a non-trivial solution are:

If $\alpha, \beta, \gamma$ $(\alpha < \beta < \gamma)$ are the values of $x$ such that $\begin{vmatrix} x-2 & 0 & 1 \\ 1 & x+3 & 2 \\ 2 & 0 & 2x-1 \end{vmatrix} = 0$ is a singular matrix,then $2\alpha + 3\beta + 4\gamma = $

If $A$ and $B$ are square matrices of order $3$ such that $|A| = -1$ and $|B| = 3$,then find the value of $|3AB|$.

Let $S$ be the set of all values of $\theta \in [-\pi, \pi]$ for which the system of linear equations
$x + y + \sqrt{3} z = 0$
$-x + (\tan \theta) y + \sqrt{7} z = 0$
$x + y + (\tan \theta) z = 0$
has a non-trivial solution. Then $\frac{120}{\pi} \sum_{\theta \in S} \theta$ is equal to

If $\left| \begin{array}{ccc} 3x - 8 & 3 & 3 \\ 3 & 3x - 8 & 3 \\ 3 & 3 & 3x - 8 \end{array} \right| = 0$,then the values of $x$ are