Eight students A, B, C, D, E, F , G and H sit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order. B and D sit neither adjacent to C nor opposite to C. A sits in between E and D, and F sits in between B and H. Which one of the following is definitely correct?

The correct option is None of the above.

To determine which statement is definitely correct, let us analyze the constraints and construct the possible seating arrangements. Let the eight seats around the circular table be numbered 1 to 8 in clockwise order. Since the table is circular, we can place the first student at any position without loss of generality.

Step 1: Placement of A, D, and E
We are given that A sits in between E and D. Let us place A at seat 1. This gives us two possible cases for the placement of E and D:
• Case 1: E is at seat 8, and D is at seat 2.
• Case 2: D is at seat 8, and E is at seat 2.

Step 2: Analysis of Case 1 (E at seat 8, A at seat 1, D at seat 2)
We need to place F, B, and H such that F sits in between B and H. This means B, F, and H must occupy three consecutive seats: either (B, F, H) or (H, F, B) in clockwise order.
The remaining empty seats are 3, 4, 5, 6, and 7. The available blocks of three consecutive seats are:
• Seats 3, 4, 5 (with F at seat 4, and B, H at seats 3, 5)
• Seats 4, 5, 6 (with F at seat 5, and B, H at seats 4, 6)
• Seats 5, 6, 7 (with F at seat 6, and B, H at seats 5, 7)

We must also satisfy the condition: B and D sit neither adjacent to C nor opposite to C.
Since D is at seat 2:
• C cannot be adjacent to D (so C cannot be at seat 3).
• C cannot be opposite to D (since seat 2 is opposite to seat 6, C cannot be at seat 6).

Let us test the consecutive seating configurations:

Configuration A: B at seat 5, F at seat 4, H at seat 3
The remaining seats for C and G are 6 and 7. Since C cannot sit at seat 6 (opposite D) and cannot sit at seat 3 (occupied), we place C at seat 7 and G at seat 6.
Let's check the rules for this arrangement:
• Seats: A(1), D(2), H(3), F(4), B(5), G(6), C(7), E(8)
• Is B (5) adjacent to C (7)? No.
• Is B (5) opposite to C (7)? No (opposite of 5 is 1).
• Is D (2) adjacent to C (7)? No.
• Is D (2) opposite to C (7)? No (opposite of 2 is 6).
This is a valid arrangement. In this arrangement, E (8) is opposite to F (4).

Configuration B: B at seat 7, F at seat 6, H at seat 5
The remaining seats for C and G are 3 and 4. Since C cannot sit at seat 3 (adjacent to D), we place C at seat 4 and G at seat 3.
Let's check the rules for this arrangement:
• Seats: A(1), D(2), G(3), C(4), H(5), F(6), B(7), E(8)
• Is B (7) adjacent to C (4)? No (adjacent seats are 6 and 8).
• Is B (7) opposite to C (4)? No (opposite of 7 is 3).
• Is D (2) adjacent to C (4)? No (adjacent seats are 1 and 3).
• Is D (2) opposite to C (4)? No (opposite of 2 is 6).
This is also a valid arrangement. In this arrangement, E (8) is opposite to C (4), and F (6) is opposite to G (3).

Conclusion:
Because both arrangements are fully consistent with all constraints given in the question, we have multiple valid seating positions:
• In the first valid arrangement, E sits opposite to F.
• In the second valid arrangement, E sits opposite to C, not F.

Thus, none of the specific choices ("B sits in between A and G", "C sits opposite to G", or "E sits opposite to F") are definitely correct in all possible scenarios. Therefore, the correct statement is None of the above.