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

Nine persons K, J, Y, R, D, L, X, P and S sit around a circular table but not necessarily in the same order. All of them are facing away from the centre of the table. K sits 3rd to the left of J. One person sits between K and X. Two persons sit between K and L. D sits immediately right of R and both of them are not adjacent to L. At least three persons sit between P and Y (both from left or right) . Y is not adjacent to

Four of the following five pair are alike in a certain way and thus forms a group, then which among the following pair doesn’t belong to that group?

The correct option is R, J.

Step-by-Step Explanation:

Let us arrange the nine persons (K, J, Y, R, D, L, X, P, and S) around a circular table facing away from the centre.
When facing away from the centre:
- Left corresponds to the clockwise direction.
- Right corresponds to the counter-clockwise direction.

1. Position J and K:
Let J sit at Seat 1. Since K sits $3$rd to the left of J, moving clockwise by $3$ positions places K at Seat $4$.

2. Position L:
Two persons sit between K (Seat 4) and L. Moving clockwise by $3$ positions gives Seat $7$ for L (since moving counter-clockwise by 3 leads to Seat 1, which is already occupied by J).

3. Position X:
One person sits between K (Seat 4) and X. X can be at Seat 2 or Seat 6.
If X were at Seat 2, there would be no adjacent empty seats available for D and R such that neither is adjacent to L (Seat 7). Thus, X must be at Seat $6$.

4. Position R and D:
D sits immediately to the right (counter-clockwise) of R, and neither is adjacent to L (Seat 7).
The available adjacent seats not next to L are Seat $3$ and Seat $2$.
Therefore, R sits at Seat $3$ and D sits at Seat $2$.

5. Position P, Y, and S:
At least three persons sit between P and Y. The remaining empty seats are 5, 8, and 9.
Seats $5$ and $9$ have exactly 3 persons between them on one side (Seats 6, 7, 8). Thus, P and Y occupy Seats 5 and 9, which leaves S at Seat $8$.
This places Y at Seat $5$ (adjacent to K) and P at Seat $9$ (adjacent to J).

Final Seating Order (Clockwise from Seat 1 to 9):
Seat 1: J
Seat 2: D
Seat 3: R
Seat 4: K
Seat 5: Y
Seat 6: X
Seat 7: L
Seat 8: S
Seat 9: P

Analyzing the Given Pairs:
- K, R: K (Seat 4) and R (Seat 3) are immediate neighbors.
- S, L: S (Seat 8) and L (Seat 7) are immediate neighbors.
- Y, K: Y (Seat 5) and K (Seat 4) are immediate neighbors.
- J, P: J (Seat 1) and P (Seat 9) are immediate neighbors.
- R, J: R (Seat 3) and J (Seat 1) are not immediate neighbors (D sits between them).

Thus, the pair R, J does not belong to the group.