Directions: Read the following information carefully and answer the given questions accordingly. Eighteen students are divided into six different groups viz., Red, Violet, Brown, Orange, Purple and Olive. They are sitting in a linear row and facing north direction. Each group consists of three students. A, B, C, D, E and F are captains of their groups. The distance between any two adjacent groups is equal. Other group members are G, H, I, J, K, L, M, N, O, P, Q and R. G, C and P belong to Violet group. Two groups are sitting between Brown and Purple groups. Neither Brown nor Purple group sits at either end. Orange group sits between Brown and Violet groups. Red group is third to the left of Olive group. A and D belong to Olive and Orange group, respectively. D sits to the left of C. Nine members are sitting between B and E, who belongs to Purple group. F is captain of O and M. K and I belong to the same group, but neither Orange nor Purple group. H and L belong to the group that is to the left of D. R is not a member of Purple group. J and E do not belong to the same group. B doesn't belong to Brown group. B and H belong to the ________

### Concept & Linear Arrangement This is a complex linear arrangement problem combined with group classification. The key is to map out the positions of the groups first and then deduce the members using elimination. ### Step-by-Step Solution * **Group Positions:** * Let the positions be 1 to 6 from left to right. * Brown and Purple are separated by two groups and neither is at an end, so they must occupy positions 2 and 5. * Red is third to the left of Olive. The only available pair with a distance of 3 (excluding 2 and 5) is 1 and 4. Thus, Red is at 1 and Olive is at 4. * Positions 3 and 6 remain. Orange is between Brown and Violet. This requires Violet to be at 6, Orange at 3, and Brown at 2. Consequently, Purple is at 5. * **Group Sequence:** 1-Red, 2-Brown, 3-Orange, 4-Olive, 5-Purple, 6-Violet. * **Assigning Members:** * Violet(6) = {C, G, P}. * 9 members (3 groups) sit between B and E(Purple, 5). So B is at 1 (Red). Red(1) = {B, ?, ?}. * Orange(3) = {D, ?, ?}. Olive(4) = {A, ?, ?}. * Captain F has O and M. The only available empty group for a captain is Brown(2). Brown(2) = {F, O, M}. * H and L are left of D(Orange). They must be in Red(1). Red(1) = {B, H, L}. * K and I are together, not in Orange/Purple. They fit in Olive(4). Olive(4) = {A, K, I}. * Remaining: J, N, Q, R. R is not in Purple, so R is in Orange. J is not with E(Purple), so J is in Orange. Orange(3) = {D, J, R}. * Purple(5) = {E, N, Q}. * **Answering the Question:** * Based on our deduction, the Red group at Position 1 consists of members B, H, and L. * Therefore, both B and H belong to the Red group. ### Exam Strategy & Shortcut By strategically tracking left/right constraints, you can identify that "H and L belong to the group to the left of D". Since D is in Orange (Position 3), the groups to the left are Brown (Position 2) and Red (Position 1). With Brown occupied by {F, O, M}, H and L must default to Red alongside B. ### Common Pitfall Failing to cross-reference positional clues (like "left of D") with group capacity. Every group has exactly 3 members, which heavily restricts where floating members can be placed. ### Final Answer Therefore, the correct answer is **Red group**.