If $A=\left(\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right)$, then $A^{10}$ is equal to

If $f(x)=\left|\begin{array}{ccc}x-3 & 2 x^2-18 & 2 x^3-81 \\ x-5 & 2 x^2-50 & 4 x^3-500 \\ 1 & 2 & 3\end{array}\right|$, then $f(\mathrm{l}) \cdot f(3)+f(3) \cdot f(5)+f(5) \cdot f(\mathrm{l})$ is

If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ $\operatorname{matrix} A$ and $|A|=4$, then $\alpha$ is equal to

If $A=\left|\begin{array}{cc}x & 1 \\ 1 & x\end{array}\right|$ and $B=\left|\begin{array}{ccc}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|$, then $\frac{d B}{d x}$ is