Study the following information carefully and answer the questions given below-

Six persons A, B, C, D, E and F sit around a circular table facing the centre but not necessarily in the same order. They like different flowers viz. Rose, Daisy, Lily, Jasmine, Marigold and Dahila but not necessarily in the same order.

F sits 2nd to the left of the one who likes Rose. B and the one who likes Rose are immediate neighbours. A faces the one who likes Jasmine and sits near F. C sits 2nd to the left of the one who likes Lily. The one who likes Dahila sits just right of the one who likes Daisy. C and D are not an immediate neighbour.

Which of the following is true?
I. D and F are not an immediate neighbour
II. A likes Lily
III. D does not like Rose

To determine which of the statements are true, let us analyze the given clues step-by-step to reconstruct the seating arrangement of the six persons (A, B, C, D, E, F) and their preferred flowers (Rose, Daisy, Lily, Jasmine, Marigold, Dahlia) around a circular table facing the centre.

Let the six positions around the circle be numbered 1 to 6 in a clockwise direction. Since they face the centre, "left" means moving clockwise, and "right" means moving counter-clockwise.

Step 1: Place F and the one who likes Rose.
Let us place the person who likes Rose at position 1.
Since F sits 2nd to the left of the one who likes Rose, F must be at position 3 (moving clockwise from position 1 by two steps: 1 → 2 → 3).
Current arrangement:
- Position 1: [Rose]
- Position 3: F

Step 2: Place B.
B and the one who likes Rose are immediate neighbours. This means B can be at position 2 or position 6.
Let us evaluate these cases.

Step 3: Analyze A's position.
We are told: "A faces the one who likes Jasmine and sits near F."
"Sits near F" means A must be adjacent to F. Since F is at position 3, A's possible positions are 2 or 4.
Also, A faces the one who likes Jasmine. In a 6-person circular table, the person sitting opposite to position $x$ is at position $(x+3)$ (modulo 6).
- If A is at position 2: A faces the person at position 5. So the person at position 5 must like Jasmine.
- If A is at position 4: A faces the person at position 1. But the person at position 1 likes Rose, not Jasmine. Thus, A cannot be at position 4.
Therefore, A must be at position 2, and the person at position 5 likes Jasmine.
Since A is at position 2, and B must be adjacent to position 1 (Rose), B must be at position 6 (as position 2 is now occupied by A).
Current arrangement:
- Position 1: [Rose]
- Position 2: A
- Position 3: F
- Position 5: [Jasmine]
- Position 6: B

Step 4: Place C and D.
The remaining positions to be filled by persons are position 1, position 4, and position 5.
We are given: "C and D are not an immediate neighbour."
Also: "C sits 2nd to the left of the one who likes Lily."
Let us find the position of Lily and C:
- If the person at position 1 (Rose) likes Lily: Not possible, since each person likes only one flower.
- If the person at position 2 (A) likes Lily:
C sits 2nd to the left of A. Moving 2 steps clockwise from position 2 gives position 4. So C would be at position 4.
Let's check this: If C is at position 4, then the remaining persons D and E must be placed in the remaining vacant positions (position 1 and position 5).
If C is at position 4, its immediate neighbours are position 3 (F) and position 5. Since C and D cannot be immediate neighbours, D cannot be at position 5. Thus, D must be at position 1, and E must be at position 5.
Let's check this configuration:
- Position 1: D [Rose]
- Position 2: A [Lily]
- Position 3: F
- Position 4: C
- Position 5: E [Jasmine]
- Position 6: B
Here, C is at position 4, and D is at position 1. They are not adjacent, which satisfies the condition. D is at position 1 and F is at position 3, so they are not immediate neighbours either.

Step 5: Place the remaining flowers (Dahlia, Daisy, Marigold).
We are given: "The one who likes Dahlia sits just right of the one who likes Daisy."
"Just right" means 1 step counter-clockwise.
Let's look at the remaining flowers for the remaining positions (positions 3, 4, 6):
The positions without assigned flowers are 3 (F), 4 (C), and 6 (B).
We need to assign Daisy and Dahlia to adjacent positions such that Dahlia is just right of Daisy (Daisy → Dahlia going counter-clockwise).
- If Daisy is at position 4 (C), Dahlia must be at position 3 (F) (just right of 4). This fits perfectly!
Then the remaining flower, Marigold, must be liked by B at position 6.
Let's double check the assignments:
- Position 1: D likes Rose
- Position 2: A likes Lily
- Position 3: F likes Dahlia
- Position 4: C likes Daisy
- Position 5: E likes Jasmine
- Position 6: B likes Marigold

Let's verify all conditions with this final layout:
1. F (3) sits 2nd to the left of D (1) who likes Rose: Yes (1 → 2 → 3 is clockwise/left).
2. B (6) and D (1) [Rose] are immediate neighbours: Yes.
3. A (2) faces E (5) who likes Jasmine, and sits near F (3): Yes.
4. C (4) sits 2nd to the left of A (2) who likes Lily: Yes (2 → 3 → 4 is clockwise/left).
5. C (4) [Daisy] and F (3) [Dahlia]: Dahlia is just right of Daisy (4 to 3 is counter-clockwise/right): Yes.
6. C (4) and D (1) are not immediate neighbours: Yes.

Step 6: Evaluate the statements.
- Statement I: D and F are not an immediate neighbour. D is at position 1 and F is at position 3. They are indeed not immediate neighbours. (True)
- Statement II: A likes Lily. A is at position 2 and likes Lily. (True)
- Statement III: D does not like Rose. D is at position 1 and likes Rose. (False)

Thus, both I and II are true.