The number of stereoisomers formed in a reaction of $$(±)\mathrm{Ph}(\mathrm{C}=\mathrm{O}) \mathrm{C}(\mathrm{OH})(\mathrm{CN}) \mathrm{Ph}$$ with $$\mathrm{HCN}$$ is ___________.

$$\left[\right.$$where $$\mathrm{Ph}$$ is $$-\mathrm{C}_{6} \mathrm{H}_{5}$$]

If $$z \neq 0$$ be a complex number such that $$\left|z-\frac{1}{z}\right|=2$$, then the maximum value of $$|z|$$ is :

Which of the following matrices can NOT be obtained from the matrix $$\left[\begin{array}{cc}-1 & 2 \\ 1 & -1\end{array}\right]$$ by a single elementary row operation ?

If the system of equations

$$ \begin{aligned} &x+y+z=6 \\ &2 x+5 y+\alpha z=\beta \\ &x+2 y+3 z=14 \end{aligned} $$

has infinitely many solutions, then $$\alpha+\beta$$ is equal to