P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as ________.

The correct option is "βα and ββ".

Let us break down the logical reasoning step-by-step to understand why this is the correct coding scheme.

We are given four distinct elements: $P$, $Q$, $R$, and $S$.
These elements must be uniquely coded using only two symbols: $\alpha$ and $\beta$.

To uniquely identify four different elements using a combination of two symbols, each code must be of length 2.
The total number of possible unique combinations of length 2 using the symbols $\alpha$ and $\beta$ is given by:
$2^2=4$ combinations.

These four possible unique codes are:
1. $\alpha \alpha$
2. $\alpha \beta$
3. $\beta \alpha$
4. $\beta \beta$

According to the problem statement:
- $P$ is coded as $\alpha \alpha$.
- $Q$ is coded as $\alpha \beta$.

Since the coding must be unique, the codes already assigned to $P$ and $Q$ cannot be reused for $R$ and $S$.
This leaves exactly two remaining codes for $R$ and $S$:
$\beta \alpha$ and $\beta \beta$.

Therefore, $R$ and $S$, respectively, can be coded as βα and ββ (or vice versa, representing the unique set of codes).