If $$A=\left[\begin{array}{llll}\sqrt{2020} & \sqrt{2021} & \sqrt{2021} & \sqrt{2023} \\ \sqrt{4040} & \sqrt{4042} & \sqrt{4044} & \sqrt{4046} \\ \sqrt{6060} & \sqrt{6063} & \sqrt{6066} & \sqrt{6069} \\ \sqrt{8080} & \sqrt{8084} & \sqrt{8088} & \sqrt{8092}\end{array}\right]$$, then the rank of $$A$$ is

If $$\left|\begin{array}{lll}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$$ and $$x, y$$ and $$z$$ are all distinct, then $$x y z$$ is equal to

Let A be a $$n\times n$$ matrix such that A is upper-triangular. Then, $$adj (A)$$ is equal to

Let $$Z_1, Z_2$$ and $$Z_3$$ be three non zero complex numbers such that $$a=\left|Z_1\right|, b=\left|Z_2\right|$$ and $$c=\left|Z_3\right|$$, if the determinant $$\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=0$$, then