JEE Math Practice Question

The values of $$m, n$$, for which the system of equations $$\begin{aligned} & x+y+z=4, \\ & 2 x+5 y+5 z=17, \\ & x+2 y+\mathrm{m} z=\mathrm{n} \end{aligned}$$ has infinitely many solutions, satisfy the equation :

1. A.$$\mathrm{m}^2+\mathrm{n}^2-\mathrm{m}-\mathrm{n}=46$$
2. B.$$\mathrm{m}^2+\mathrm{n}^2+\mathrm{mn}=68$$
3. C.$$\mathrm{m}^2+\mathrm{n}^2-\mathrm{mn}=39$$
4. D.$$\mathrm{m}^2+\mathrm{n}^2+\mathrm{m}+\mathrm{n}=64$$