If $\Delta =\begin{vmatrix} \cos \theta /2 & 1 & 1\\ 1 & \cos \theta /2 & -\cos \theta /2\\ -\cos \theta /2 & 1 & -1 \end{vmatrix}$, If the minimun of $\Delta$ is $m_{1}$ and maximum of $\Delta$ is $m_{2}$, then $\left [ m_{1}, m_{2} \right ]$ are related

If the points $(2,5),(4,6)$ and $(a,a)$ are collinear, then the value of $a$ is equal to

  $\left \lvert \begin{matrix} 1 & - 1 & 2 \\ 2 & - 2 & 1 \\ - 3 & 4 & - 5 \end{matrix} \right \rvert$   এ (3, 1) তম ভুক্তির সহগুণক কত?

Three digits numbers $7x,36y$ and $12z$ where $x , y , z$ are integers from $0$ to $9 ,$ are divisible by a fixed constant $k.$ Then the determinant $\left| \begin{array} { l l l } { x } & { 3 } & { 1 } \\ { 7 } & { 6 } & { z } \\ { 1 } & { y } & { 2 } \end{array} \right|$ $\ +48$ must be divisible by

$\mathrm{K}$ এর কোন মানের জন্য $\left[\begin{array}{cc}K+1 & 3 \\ 3 & K-1\end{array}\right]$ ম্যাট্রিক্সটি বিপরীতযোগ্য নয়?