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 $\mathrm{b}+\mathrm{c}=$

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

The value of $\displaystyle \left | \begin{matrix} 11 & 12 & 13 \\ 12&13&14 \\ 13&14&15 \end{matrix} \right |$ is,

Find the values of $k,$ if the points $A (k + 1, 2k), B (3k, 2k + 3)$ and $C (5k +1, 5k)$ are collinear.