Which among the following statement(s) is /are true?
I. D is the only neighbour of C II. More than three persons sit to the right of Q III. No one sits to the left of E Study the following information carefully and answer the given questions below:
Twelve persons sit in two parallel rows such that six persons sit in each row. In row 1- A, B, C, D, E and F sit and face north direction and in row 2- M, N, O, P, Q and R sit and face south direction. The persons sit in row 1 face the persons sit in row 2 and vice versa.
A sits third to the right of the one who faces Q. Only two persons sit between A and E. Even number of persons sit between Q and M. P sits to the immediate left of M. R sits to the immediate right of M. The one who faces R sits second to the left of D. B and F sit adjacent to each other. B doesn’t face R. N doesn’t sit next to Q.

To determine which of the given statements is/are true, let us step-by-step deduce the exact seating arrangement of the 12 persons in two parallel rows.

Understanding the Setup:
- Row 1 (facing North): A, B, C, D, E, F
- Row 2 (facing South): M, N, O, P, Q, R
Each row contains 6 positions (from left to right, 1 to 6).

Step 1: Analyzing the positions in Row 2 and Row 1 based on A and Q.
- "A sits third to the right of the one who faces Q."
Since persons in Row 1 face North (Right is towards position 6):
If the person facing Q is at position 1 of Row 1, then A is at position 1 + 3 = 4.
If the person facing Q is at position 2 of Row 1, then A is at position 2 + 3 = 5.
If the person facing Q is at position 3 of Row 1, then A is at position 3 + 3 = 6.
Thus, Q in Row 2 can be at position 1, 2, or 3.

- "Only two persons sit between A and E."
If A is at position 4: E must be at position 1 (4 - 3 = 1).
If A is at position 5: E must be at position 2 (5 - 3 = 2).
If A is at position 6: E must be at position 3 (6 - 3 = 3).

Step 2: Placing M, P, and R in Row 2.
- "P sits to the immediate left of M. R sits to the immediate right of M."
Since Row 2 faces South, for persons in Row 2, 'Right' is towards position 1 and 'Left' is towards position 6.
Therefore, R, M, and P sit in consecutive order from left to right as: R - M - P (occupying 3 contiguous seats).

- "Even number of persons sit between Q and M."
The number of persons between Q and M can be 0, 2, or 4.
- "The one who faces R sits second to the left of D."
Since persons in Row 1 face North, left is towards position 1. So if D is at position x, the person facing R is at position x - 2. This means R cannot be at position 1 or 2 in Row 2 (since x - 2 ≥ 1 ⇒ x ≥ 3).

Let us test the possible positions for Q:

Case 1: Q is at Position 1
If Q is at Position 1, the person facing Q is at Position 1 in Row 1.
Then A is at Position 4, and E is at Position 1.
However, E and the person facing Q would both be at Position 1 in Row 1. But Q faces position 1, which means E faces Q. This is valid.
Next, since Q is at position 1, and the number of persons between Q and M is even (0, 2, or 4):
- If 0 persons between Q and M: M would be at position 2. Then R (immediate right of M) would be at position 1, which conflicts with Q being at position 1.
- If 2 persons between Q and M: M is at position 4. Then R is at position 3, and P is at position 5. The block R-M-P occupies positions 3-4-5.
Let's check this placement:
Row 2: Q(1), _(2), R(3), M(4), P(5), _(6)
Number of persons between Q(1) and M(4) is 2 (positions 2 and 3), which is even!
The person facing R is at Position 3 in Row 1. Since this person sits second to the left of D, D must be at Position 5 (5 - 2 = 3).
Currently, Row 1 has: E(1), _(2), _(3), A(4), D(5), _(6).
- "B and F sit adjacent to each other. B doesn’t face R."
Row 1 has empty spots at positions 2, 3, 6.
Since B and F are adjacent, they must occupy positions 2 and 3.
Position 3 faces R. Since B cannot face R, B must be at Position 2, and F must be at Position 3.
Then C must occupy the remaining spot in Row 1, which is Position 6.
Row 1: E(1), B(2), F(3), A(4), D(5), C(6).

Now for Row 2:
Positions filled so far: Q(1), _(2), R(3), M(4), P(5), _(6).
The remaining empty spots are positions 2 and 6.
- "N doesn’t sit next to Q."
Position 2 is next to Q (Position 1), so N cannot be at Position 2.
Thus, N must be at Position 6, and O must be at Position 2.
Row 2: Q(1), O(2), R(3), M(4), P(5), N(6).

Final Seating Arrangement Verification:
Row 2 (facing South): Q(1) - O(2) - R(3) - M(4) - P(5) - N(6)
Row 1 (facing North): E(1) - B(2) - F(3) - A(4) - D(5) - C(6)

Let me re-verify all conditions:
1. A(4) sits third to the right of E(1) who faces Q(1): Correct.
2. Two persons (B, F) sit between A(4) and E(1): Correct.
3. Even number of persons (O, R = 2 persons) between Q(1) and M(4): Correct.
4. P(5) is to the immediate left of M(4), R(3) is to the immediate right of M(4): Correct (facing South).
5. Person facing R is F(3), who sits second to the left of D(5): Correct.
6. B(2) and F(3) sit adjacent to each other, B doesn't face R: Correct.
7. N(6) doesn't sit next to Q(1): Correct.

Evaluating the Statements:
- Statement I: D is the only neighbour of C.
C is at position 6 (extreme right end of Row 1). Its only neighbour is D (at position 5).
$\text{Statement I is TRUE.}$

- Statement II: More than three persons sit to the right of Q.
Q faces South and is at position 1 (the extreme right end when facing South).
To the right of Q (towards position 1 / beyond position 1): 0 persons sit to the right of Q.
$\text{Statement II is FALSE.}$

- Statement III: No one sits to the left of E.
E is at position 1 (the extreme left end of Row 1 facing North).
Therefore, 0 persons sit to the left of E.
$\text{Statement III is TRUE.}$

Thus, statements I and III are true.

The correct answer is Both I and III.