Given:
$g(n) \in \Theta(n^3)$
This means $g(n)$ grows exactly like $n^3$ up to constant factors.
Now check each statement.
$\text{S1}$: $g(n) \in O(n^3)$
This is true.
If $g(n) \in \Theta(n^3)$, then it automatically means:
$g(n) \in O(n^3)$
So, $\text{S1}$ is true.
$\text{S2}$: $g(n) \in \Theta(n)$
This is false.
$g(n)$ grows like $n^3$, not like $n$.
So, $\text{S2}$ is false.
$\text{S3}$: $g(n) \in \Omega(n)$
This is true.
Since $n^3$ grows faster than $n$, any function growing like $n^3$ is also lower bounded by $n$.
So, $g(n) \in \Omega(n)$
Therefore, true statements are: $\text{S1}$ and $\text{S3}$
Answer : B
