If maximum and minimum values of $D=\left|\begin{array}{ccc}1 & -\cos \theta & \\ \cos \theta & 1 & -\cos \theta \\ 1 & \cos \theta & 1\end{array}\right|$ are $p$ and $q$ respectively, then the value of $2 p+3 q$ is-

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

lf the lines $3\mathrm{x}+2\mathrm{y}-5=0,\ 2\mathrm{x}-5\mathrm{y}+3=0,\ 5\mathrm{x}+\mathrm{b}\mathrm{y}+\mathrm{c}=0$ are concurrent then $\mathrm{b}+\mathrm{c}=$

If x, y, z are in A.P., then the value of the det A. ;Where ;A=$\begin{vmatrix} 4 &5 & 6 & x\\ 5& 6 & 7 &y \\ 6& 7& 8 &z \\ x & y & z & 0 \end{vmatrix}$ 

$A=\left[\begin{array}{ccc}a^{2} & b c & c a+c^{2} \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right]$ একটি নির্ণায়ক এবং $g(x)=x^{2}+3 x$.