Which among the following statement(s) is/are true?
I. O is the only neighbour of P
II. N sits exactly between O and Q
III. More than one person sit to the right of Q
Study the following information carefully and answer the questions given below:
Seven persons -M, N, O, P, Q, R and S sit in a linear row and facing the north but not necessarily in the same order.
Only four persons sit between P and Q who does not sit at the extreme end of the row. S sits to the immediate right of Q. The number of persons sitting to the right of S is same as the number of persons sitting between M and N who sits to the immediate left of R. O sits to the left of R.

To determine which statements are true, let us reconstruct the seating arrangement step-by-step based on the given clues.

We have seven persons: M, N, O, P, Q, R, and S, sitting in a linear row facing North. Let the positions in the row be numbered 1 to 7 from left to right.

Step 1: Analyze the positions of P and Q.
Clue: Only four persons sit between P and Q. Q does not sit at the extreme end of the row.
Since there are seven positions in total, a gap of four persons between P and Q means if one is at position x, the other is at position x + 5.
The possible pairs of positions for (P, Q) or (Q, P) are:
- 1 and 6
- 2 and 7
Since Q cannot sit at either extreme end (positions 1 or 7), Q must sit at position 6 (if P is at 1) or position 2 (if P is at 7). This gives us two cases:
- Case 1: P is at 1, Q is at 6.
- Case 2: Q is at 2, P is at 7.

Step 2: Place S using the next clue.
Clue: S sits to the immediate right of Q.
- In Case 1: Q is at 6, so S must be at position 7.
- In Case 2: Q is at 2, so S must be at position 3.

Step 3: Analyze the positions of M, N, and R.
Clue: N sits to the immediate left of R. This means we must place the pair (N, R) in two adjacent vacant seats in that order (N followed by R).
Clue: The number of persons sitting to the right of S is same as the number of persons sitting between M and N.
Let us evaluate this clue for both cases:

Evaluating Case 1:
P is at 1, Q is at 6, S is at 7.
Row: [P, _, _, _, _, Q, S]
The number of persons sitting to the right of S (position 7) is 0.
Therefore, the number of persons sitting between M and N must also be 0. This means M and N must sit adjacent to each other.
Since N is immediately to the left of R, we need three adjacent positions for (M, N, R) or (N, R, M) to satisfy the adjacency conditions. The vacant positions in Case 1 are 2, 3, 4, and 5.
Let us try to place them:
If M, N, R occupy positions 2, 3, and 4 (or some permutation):
Since N sits immediately left of R, N and R must be at (2, 3), (3, 4), or (4, 5).
Since the number of persons between M and N must be 0, M must be adjacent to N.
- If N is at 3 and R is at 4: M can be at 2. This leaves position 5 for O. Let's check the order: P at 1, M at 2, N at 3, R at 4, O at 5, Q at 6, S at 7.
Check the final clue: O sits to the left of R. But here, O is at position 5 and R is at position 4, so O is to the right of R. This is invalid.
- If N is at 4 and R is at 5: M can be at 3. This leaves position 2 for O. Let's check the order: P at 1, O at 2, M at 3, N at 4, R at 5, Q at 6, S at 7. Here, O (at 2) is to the left of R (at 5). This satisfies all conditions!

Let's double-check the configuration for Case 1:
Positions: 1: P, 2: O, 3: M, 4: N, 5: R, 6: Q, 7: S
- Four persons between P (1) and Q (6): O, M, N, R (Correct).
- Q is not at the end (Correct).
- S (7) is to the immediate right of Q (6) (Correct).
- Persons to the right of S: 0 (Correct).
- N (4) is to the immediate left of R (5) (Correct).
- Persons between M (3) and N (4): 0 (Correct, which matches the number of persons to the right of S).
- O (2) is to the left of R (5) (Correct).

For completeness, let's check Case 2: Q is at 2, S is at 3, P is at 7.
Row: [_, Q, S, _, _, _, P]
The number of persons to the right of S (at 3) is 4 (positions 4, 5, 6, 7).
Thus, there must be 4 persons between M and N. This requires M and N to be separated by 4 seats, which is impossible with the remaining vacant positions (1, 4, 5, 6). So, Case 2 is invalid.

Thus, the unique final arrangement from left to right is:
P - O - M - N - R - Q - S

Step 4: Evaluate the statements.
- Statement I: O is the only neighbour of P. Since P is at the extreme left (position 1) and O is at position 2, P has only one neighbour, which is O. (True)
- Statement II: N sits exactly between O and Q. O is at position 2, Q is at position 6. The position exactly between 2 and 6 is $\frac{2+6}{2}=4$, which is occupied by N. (True)
- Statement III: More than one person sit to the right of Q. Only S (1 person) sits to the right of Q. (False)

Therefore, only statements I and II are true.