JEE Math Practice Question

Let S$$_1$$ and S$$_2$$ be respectively the sets of all $$a \in \mathbb{R} - \{ 0\} $$ for which the system of linear equations $$ax + 2ay - 3az = 1$$ $$(2a + 1)x + (2a + 3)y + (a + 1)z = 2$$ $$(3a + 5)x + (a + 5)y + (a + 2)z = 3$$ has unique solution and infinitely many solutions. Then

1. A.$$\mathrm{n({S_1}) = 2}$$ and S$$_2$$ is an infinite set
2. B.$$\mathrm{{S_1} = \Phi} $$ and $$\mathrm{{S_2} = \mathbb{R} - \{ 0\}}$$
3. C.$$\mathrm{{S_1} = \mathbb{R} - \{ 0\}}$$ and $$\mathrm{{S_2} = \Phi} $$
4. D.S$$_1$$ is an infinite set and n(S$$_2$$) = 2