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 sits in between B and H. Which one of the following is definitely correct?

The problem asks us to identify a statement that is "definitely correct" based on the given seating arrangement conditions. This means the statement must be true for all possible valid arrangements. If we can find even one valid arrangement where an option is false, then that option is not definitely correct.

Let's list the conditions:

1. Eight students A, B, C, D, E, F, G, H sit around a circular table, equidistant, facing the centre.
2. B and D sit neither adjacent to C nor opposite to C.
3. A sits in between E and D (forming a block E-A-D or D-A-E).
4. G sits in between B and H (forming a block B-G-H or H-G-B).

The most restrictive condition is condition 2. Let's assume C is at position 1 (out of 8 positions).

• Adjacent positions to C are 2 and 8.
• The opposite position to C is 5. Therefore, B and D cannot be at positions 2, 8, or 5. This means B and D must be chosen from positions 3, 4, 6, or 7.

We have two blocks of three consecutive people: (E A D) and (B G H). The remaining two people are C and F.

Let's try to construct a valid arrangement: Arrangement 1:

1. Place C at position 1.
2. Place the block (E A D) starting at position 2: E(2), A(3), D(4).
   • Here, D is at position 4, which is allowed (not 2, 8, or 5).
3. Place the block (B G H) starting at position 6: B(6), G(7), H(8).
   • Here, B is at position 6, which is allowed (not 2, 8, or 5).
4. The remaining person, F, must be at position 5.
   • This arrangement is: C(1) E(2) A(3) D(4) F(5) B(6) G(7) H(8).
   • Let's verify condition 2: C is at 1. D is at 4 (not adjacent or opposite to C). B is at 6 (not adjacent or opposite to C). All conditions are satisfied. This is a valid arrangement.

Now, let's check the given options against Arrangement 1: A) B sits in between A and G.

• In Arrangement 1: A is at 3, B is at 6, G is at 7. The sequence is A-D-F-B-G. B is not between A and G. (False) B) C sits opposite to G.
• In Arrangement 1: C is at 1, G is at 7. Opposite to 1 is 5. C is not opposite to G. (False) C) E sits opposite to F.
• In Arrangement 1: E is at 2, F is at 5. Opposite to 2 is 6. E is not opposite to F. (False)

Since options A, B, and C are all false for this valid arrangement, none of them can be "definitely correct". Therefore, option D (None of the above) must be the correct answer.

(For completeness, we can also find another valid arrangement that yields the same conclusion for the options, confirming they are not universally true.)

The final answer is D.