Algebra Questions

Let $a,b,c$ be such that $(b+a)c\ne 0$. If
$$\left|\begin{array}{ccc}a& a+1& a-1\\ b& b+1& b-1\\ c& c-1& c+1\end{array}\right|+\left|\begin{array}{ccc}a+1& b+1& c-1\\ a-1& b-1& c+1\\ (-1{)}^{n}a& (-1{)}^{n}b& (-1{)}^{n+1}c\end{array}\right|=0$$
then the value of '$n$ ' is:

If the roots of the equation $b{x}^2+cx+a=0$ be imaginary, then for all real values of $x$, the expression $3b^2{x}^2+6bcx+2c^2$ is:

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is:

If $|z-4/z|=2$, then the maximum value of $|z|$ is equal to:

The remainder left out when $8^{2n}-(62{)}^{2n+1}$ is divided by $9$ is:

The sum to the infinity of the series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+\dots$ is:

1: $\text{adj}(\text{adj }A)=A$ where $A$ is a $2\times 2$ matrix.
2: $|\text{adj }A|=|A|$.