Consider the system of equations 
 $$\begin{gathered} (\lambda -1)x+(3\lambda +1)y+2\lambda z=0 \\ (\lambda -1)x+(4\lambda -2)y+(\lambda +3)z=0 \\ 2x+(3\lambda +1)y+3(\lambda -1)z=0 \end{gathered}$$
 &  $\lambda ={\lambda }_1,{\lambda }_2,{\lambda }_3,\mathrm{......},{\lambda }_n$, $({\lambda }_1<{\lambda }_2<{\lambda }_3<\mathrm{.....}<\lambda n)$  be the possible values of  $\lambda$  for which  the system is consistent $\left(x^2+y^2+z^2\ne 0\right)$ & 
Which of the following is/are   true?
 

The number of triplets $(x,y,z)suchthat(x,y,z\in N\&1\le x,y,z\le 3)$  solution set of  given system of equation When  $\lambda ={\lambda }_2$ is 27

The number of triplets $(x,y,z)suchthat(x,y,z\in N\&1\le x,y,z\le 3)$ solution set of  given system of equation when  $\lambda ={\lambda }_1$  is 3

The number of triplets  $(x,y,z)suchthat(x,y,z\in N)$ solution set of  given system of equation   $\lambda ={\lambda }_2$ is infinitely many

$n=3$