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

If the determinant $\left|\begin{array}{ccc}\cos 2x & \sin^2 x & \cos 2x \\ \sin^2 x & \cos 2x & \cos^2 x \\ \cos 2x & \cos^2 x & \cos 2x\end{array}\right|$ is expanded in powers of $\cos x$,then the constant term in the expansion is

The number of values of $\lambda$ for which the points $(\lambda + 1, 1)$,$(2\lambda + 1, 3)$,and $(2\lambda + 2, 2\lambda)$ are collinear is:

The value of $\left| \begin{array}{ccc} 265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 \end{array} \right|$ is equal to

Let $A = \begin{bmatrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \end{bmatrix}$. If $|A|^2 = 25$, then $|\alpha|$ is equal to:

Let $\theta \in \left(0, \frac{\pi}{2}\right)$. 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: