If the system of equations $\begin{array}{l}3x+4y+5z=\mu \\ x+2y+3z=1\\ 4x+4y+4z=\delta \end{array}$is consistent, then $(\delta ,\mu )$ can be

For the given system of equations, we find that 

$D=0,D_1=-4\mu +2\delta +4,D_2=8\mu -4\delta -8$    

and $D_3=-4\mu +2\delta +4$

So, the system will be consistent if

$D_1=D_2=D_3=0\Rightarrow 2\mu =\delta +2$

Clearly, $\delta =4,\mu =3$ satisfies this equation. Hence, option ($c$) is correct.