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:

Looking at this circular seating arrangement problem with six boys facing the center.

We have $6$ boys sitting around a circular table, all facing the CENTER. When facing the center, "right" means clockwise and "left" means counter-clockwise.

Given information:

• M is second to the right of K

• M is opposite to R

• L and O are sitting opposite to each other

• Neither L nor R is sitting beside F

---

In a $6$-person circle, opposite means $3$ seats apart.

Let's place M at position $1$ and R at position $4$ (opposite to M).

Since L and O are also opposite, they occupy another pair of opposite positions.

---

M is second to the right of K means: starting from K, moving $2$ positions clockwise reaches M.

If M is at position $1$, then K must be at position $5$ (since $5 \to 6 \to 1$).

Now we have:

• Position $1$: M

• Position $4$: R

• Position $5$: K

Remaining boys: L, O, F for positions $2, 3, 6$

---

L and O are opposite. The available opposite pairs are $(2,5)$ or $(3,6)$.

Since position $5$ is taken by K, L and O must be at positions $3$ and $6$.

Constraint: Neither L nor R is beside F.

R at position $4$ is beside positions $3$ and $5$.

Position $5$ has K, so if F were at position $3$, F would be beside R (violation).

Therefore, F cannot be at position $3$. So F must be at position $2$.

This means L and O are at positions $3$ and $6$.

---

Testing which arrangement works:

If L is at position $3$ and O is at position $6$:

L at position $3$ is beside positions $2$ and $4$. Position $2$ has F, position $4$ has R.

This means L is beside both F and R (violation).

If L is at position $6$ and O is at position $3$:

L at position $6$ is beside positions $5$ and $1$. These have K and M (no F or R). ✓

R at position $4$ is beside positions $3$ and $5$. These have O and K (no F). ✓

Final arrangement: $1$:M, $2$:F, $3$:O, $4$:R, $5$:K, $6$:L

---

Checking each statement:

(A) F is sitting between M and O.

Clockwise from M$(1)$: $1 \to 2 \to 3$ gives M $\to$ F $\to$ O.

F at position $2$ is between M and O. ✓

(B) R is second to the right of L.

From L$(6)$, second position clockwise: $6 \to 1 \to 2$ gives position $2$, which is F (not R). ✗

(C) M is third to the left of R.

From M$(1)$, counter-clockwise: $1 \to 6 \to 5 \to 4$ gives R at position $4$. ✓

(D) M is third to the right of R.

From R$(4)$, clockwise: $4 \to 5 \to 6 \to 1$ gives M at position $1$. ✓

---

Statements (A), (C), and (D) are valid. Statement (B) is invalid.

Option 2: (A), (C) and (D) only