If $\sqrt{2}$ and $\sqrt{3}$ are roots of the equation $a_0 + a_1 x + a_2 x^2 + a_3 x^3 + x^4 = 0$ where $a_0, a_1, a_2, a_3$ are integers, then which one of the following is correct?

Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1 + z_2}{z_1 - z_2}\right| = 1$, then what is $\operatorname{Re} \left(\frac{z_1}{z_2}\right) + 1$ equal to?

If $26! = n8^k$, where $k$ and $n$ are positive integers, then what is the maximum value of $k$?

Consider the following statements in respect of two non-singular matrices $A$ and $B$ of the same order $n$:

1. 1.$adj(AB) = (adjA)(adjB)$


2. 2. $adj(AB) = adj(BA)$


3. 3. $(AB) adj(AB) - |AB| I_n$ is a null matrix of order $n$