Which among the following statement(s) is/are incorrect?
I. T doesn’t sit adjacent to S
II. Q sits exactly between W and V
III. U sits third to the left of Q

Study the following information carefully and answer the questions given below:
Nine persons- P, Q, R, S, T, U, V, W and X sit around the circular table, where all are facing towards the centre but not necessarily in the same order.

One person sits between Q and W. S sits third to the right of W. S and X sit adjacent to each other. R sits second to the right of X. As many persons sit between R and T as between T and U. Two persons sit between U and V who neither sits adjacent to T nor P. Q and V doesn’t sit together.

The correct option is Only II.

Step-by-Step Explanation and Seating Arrangement:

Let's analyze the given statements and place all nine persons (P, Q, R, S, T, U, V, W, X) around a circular table facing the centre.

1. Deductions from Clues:

• Clue 1: "One person sits between Q and W."
This gives two cases for Q's position relative to W (either 2 places to the left or 2 places to the right of W).

• Clue 2: "S sits third to the right of W."
Starting at position of W, moving 3 places clockwise/right gives S's position.

• Clue 3: "S and X sit adjacent to each other."
• Clue 4: "R sits second to the right of X."
• Clue 5: "As many persons sit between R and T as between T and U." (Meaning T is exactly in the middle of R and U along the circle).
• Clue 6: "Two persons sit between U and V who neither sits adjacent to T nor P."
• Clue 7: "Q and V doesn’t sit together."

2. Step-by-step Arrangement (in clockwise order around the circle):

Let's arrange the positions 1 to 9 in clockwise order facing centre:

• Position 1: W
• Position 2: P
• Position 3: Q (1 person between W and Q at pos 2)
• Position 4: S (3rd to the right of W)
• Position 5: X (Adjacent to S)
• Position 6: U
• Position 7: R (2nd to the right of X)
• Position 8: T (Midway between R and U, also T is between R at 7 and U at 6 when going counter-clockwise/clockwise)
Let's verify the exact positions around the circle clockwise from 1 to 9:
1. W
2. P
3. Q
4. S
5. X
6. V
7. R
8. T
9. U

Let's double-check all conditions for this seating order (W → P → Q → S → X → V → R → T → U clockwise):

• One person between Q and W? Yes, P is at position 2.
• S sits third to the right of W? W is 1, S is 4. Yes (1 + 3 = 4).
• S and X sit adjacent? S is 4, X is 5. Yes.
• R sits second to right of X? X is 5, R is 7. Yes.
• Number of persons between R and T equals between T and U? R is 7, T is 8, U is 9. Between R and T = 0 persons; between T and U = 0 persons. Equal! Yes.
• Two persons sit between U and V? U is 9, V is 6. Moving counter-clockwise from 9 to 6 gives positions 8(T) and 7(R), which is 2 persons. Yes.
• V does not sit adjacent to T or P? V is at 6. Adjacent positions are 5(X) and 7(R). Neither is T nor P. Yes.
• Q and V don't sit together? Q is at 3, V is at 6. They are not together. Yes.

3. Evaluating the Given Statements:

• Statement I: "T doesn’t sit adjacent to S"
T is at position 8 and S is at position 4. They are not adjacent. Thus, Statement I is CORRECT.

• Statement II: "Q sits exactly between W and V"
Between W (1) and V (6): On one side we have P (2) and Q (3). Q does not sit exactly in the middle of W and V (P is between W and Q). Thus, Statement II is INCORRECT.

• Statement III: "U sits third to the left of Q"
Q is facing the centre at position 3. Moving to the left (clockwise): 1st left is S (4), 2nd left is X (5), 3rd left is V (6)... wait, going counter-clockwise (left facing center): 1st left is P (2), 2nd left is W (1), 3rd left is U (9). So U sits third to the left of Q! Thus, Statement III is CORRECT.

Since the question asks which statement(s) is/are incorrect, only Statement II is incorrect.

Hence, the correct choice is Only II.