Consider a matrix $A={\left[a_{ij}\right]}_{3\times 3}$ where, $a_{ij}=\left\{\begin{array}{cc}i+2j& \forall ij=\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\\ 2i-3j& \forall ij=\mathrm{o}\mathrm{d}\mathrm{d}\end{array}\right.$. If $b_{ij}$ is the cofactor of $a_{ij}$ in matrix $A$ and $C_{ij}=\sum _{r=1}^3{a}_{ir}{b}_{jr}$, then ${\left[C_{ij}\right]}_{3\times 3}$ is

If $x>0, y>0$ and $z>0$ are the second, third and fourth terms of a geometric progression and $\mathit{∆}=\left|\begin{array}{lll}{x}^k& x^{k+1}& x^{k+2}\\ y^k& y^{k+1}& y^{k+2}\\ z^k& z^{k+1}& z^{k+2}\end{array}\right|={\left(r-1\right)}^2\left(1-\frac{1}{r^2}\right)$, (where $r$ is the common ratio) then

If $f\left(x\right),g\left(x\right)$ and $h\left(x\right)$ are polynomials of degree $4$ and $\left|\begin{array}{ccc}f\left(x\right)& g\left(x\right)& h\left(x\right)\\ a& b& c\\ p& q& r\end{array}\right|=m{x}^4+n{x}^3+r{x}^2+sx+t$ be an identity in $x,$then $$$\left|\begin{array}{ccc}{f}^{\text{'}\text{'}\text{'}}\left(0\right)-f^{\text{'}\text{'}}\left(0\right)& g^{\text{'}\text{'}\text{'}}\left(0\right)-g^{\text{'}\text{'}}\left(0\right)& h^{\text{'}\text{'}\text{'}}\left(0\right)-h^{\text{'}\text{'}}\left(0\right)\\ a& b& c\\ p& q& r\end{array}\right|$ is