GATE Civil Engineering

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Four persons $\text{P, Q, R}$ and $\text{S}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{R}$ cannot sit adjacent to each other. $\text{S}$ should be seated to the right of $\text{Q}$. The number of distinct seating arrangements possible is:

- $2$
- $4$
- $6$
- $8$

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Best answer

Given that, four persons $\text{P, Q, R}$ and $\text{S}$ are to be seated in a row.

- $\text{P}$ and $\text{R}$ cannot sit adjacent to each other.
- $\text{S}$ should be seated to the right of $\text{Q}$.

Now, the four persons can be seated in the below arrangements:

- $\begin{array}{|c|c|c|}\hline {\color{Red}{Q}} & P & {\color{Blue}{S}} & R \\\hline\end{array}$
- $\begin{array}{|c|c|c|}\hline {\color{Red}{Q}} & R & {\color{Blue}{S}} & P \\\hline\end{array}$
- $\begin{array}{|c|c|c|}\hline P & {\color{Red}{Q}} & {\color{Blue}{S}} & R \\\hline\end{array}$
- $\begin{array}{|c|c|c|}\hline R & {\color{Red}{Q}} & {\color{Blue}{S}} & P \\\hline\end{array}$
- $\begin{array}{|c|c|c|}\hline P & {\color{Red}{Q}} & R & {\color{Blue}{S}} \\\hline\end{array}$
- $\begin{array}{|c|c|c|}\hline R & {\color{Red}{Q}} & P & {\color{Blue}{S}} \\\hline\end{array}$

$\therefore$ The number of distinct seating arrangements possible $ = 6.$

So, the correct answer is $(C).$

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