The number of real values of ' $a$ ' for which the system of equations $2 x+3 y+a z=0, x+a y-2 z=0$ and $3 x+y+3 z=0$ has non-trivial solution is

If the eight vertices of a regular octagon are given by the complex number $\frac{1}{x_j-2 i}(j=1,2,3,4,5,6,7,8)$, then the radius of the circumcircle of the octagon is

If $\left|Z_1-3-4 i\right|=5$ and $\left|Z_2\right|=15$, then the sum of the maximum and minimum values of $\left|Z_1-Z_2\right|$ is

If $Z=r(\cos \theta+i \sin \theta),\left(\theta \neq-\frac{\pi}{2}\right)$ is solution of $x^3=i$, then $r^9(\cos \theta+i \sin \theta)^9=x^{3-}=i$