Six boys are sitting around a circular table facing the centre. M is second to the right of K, and is sitting opposite to R. L and O are sitting opposite to each other. Neither L nor R is sitting beside F. Based on the above information, the following statements are given:

(A) F is sitting between M and O.
(B) R is second to the right of L.
(C) M is third to the left of R.
(D) M is third to the right of R.

Choose the correct answer from the options given below:

(A), (C) and (D) only

The correct answer is Option (2) → (A), (C) and (D) only

To solve this, let's map out the positions around a circular table with six seats (1 through 6 in a clockwise direction).

1. Placing the Boys

• M is second to the right of K: Let's place K at Position 1. Moving two spots clockwise (right) puts M at Position 3.
• M is sitting opposite R: In a six-person circle, the opposite of Position 3 is Position 6. So, R is at Position 6.
• L and O are opposite each other: The remaining pairs of opposite seats are (1, 4) and (2, 5). Since Position 1 is already taken by K, L and O must occupy Positions 2 and 5.
• Neither L nor R is sitting beside F: Only Position 4 is left vacant, so F must be at Position 4.
• F (Pos 4) cannot be beside L. The seats adjacent to F are Pos 3 and Pos 5. Therefore, L cannot be at Pos 5.
• This means L must be at Position 2, and O must be at Position 5.

2. Final Arrangement (Clockwise)

1. K
2. L
3. M
4. F
5. O
6. R

3. Evaluating the Statements

• (A) F is sitting between M and O: F (Pos 4) is indeed between M (Pos 3) and O (Pos 5). (Correct)
• (B) R is second to the right of L: From L (Pos 2), moving two spots right takes you to F (Pos 4). R (Pos 6) is actually second to the left of L. (Incorrect)
• (C) M is third to the left of R: In a group of six, "third to the left" is the same as being "opposite." Since M and R are opposite, this is (Correct).
• (D) M is third to the right of R: Similarly, "third to the right" in a group of six also means "opposite." (Correct).

Conclusion

Statements (A), (C), and (D) are true.