The number of real values of $\lambda$ for which the system of linear equations $$2 x + 4 y - \lambda z = 0$$ $$4 x + \lambda y + 2 z = 0$$ $$\lambda x + 2 y + 2 z = 0$$ has infinitely many solutions, is:
(1) 0
(2) 1
(3) 2
(4) 3

Let the system of equations $x + 2y + 3z = 5$, $2x + 3y + z = 9$, $4x + 3y + \lambda z = \mu$ have infinite number of solutions. Then $\lambda + 2\mu$ is equal to:
(1) 28
(2) 17
(3) 22
(4) 15

Consider the system of linear equation $x + y + z = 4 \mu , x + 2 y + 2 \lambda z = 10 \mu , x + 3 y + 4 \lambda ^ { 2 } z = \mu ^ { 2 } + 15$, where $\lambda , \mu \in \mathrm { R }$. Which one of the following statements is NOT correct?
(1) The system has unique solution if $\lambda \neq \frac { 1 } { 2 }$ and $\mu \neq 1$
(2) The system is inconsistent if $\lambda = \frac { 1 } { 2 }$ and $\mu \neq 1, 15$
(3) The system has infinite number of solutions if $\lambda = \frac { 1 } { 2 }$ and $\mu = 15$
(4) The system is consistent if $\lambda \neq \frac { 1 } { 2 }$

If the system of linear equations $$\begin{aligned} & x - 2 y + z = - 4 \\ & 2 x + \alpha y + 3 z = 5 \\ & 3 x - y + \beta z = 3 \end{aligned}$$ has infinitely many solutions, then $12 \alpha + 13 \beta$ is equal to
(1) 60
(2) 64
(3) 54
(4) 58