GATE ME 2021 Set 2 — Question 1

MCQ+1 / -0.33MediumPermutations & CombinationsQuantitative AptitudeGeneral AptitudeDeduction & InductionAnalytical Aptitude

General Aptitude → Analytical Aptitude → Deduction & Induction

Last updated 5 September 2026

Question

Five persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

Correct answer (B) 3 Solution Let the five seats be represented as (1, 2, 3, 4, 5) from left to right. Given: R is at the second position from the left end. So, the arrangement is: R . Given: P and T cannot be seated at either end (1 or 5). Thus, P and T must occupy positions 3 and 4 in some order. Case 1: P is at position 3 and T is at position 4. Arrangement: R P T The remaining persons are Q and S, to be placed in positions 1 and 5. Condition: P should not be seated adjacent to S. Since P is at position 3, its neighbors are positions 2 (R) and 4 (T). S can be at position 1 or 5 without being adjacent to P. Possible arrangements for Case 1: (Q, R, P, T, S) and (S, R, P, T, Q). (2 arrangements) Case 2: T is at position 3 and P is at position 4. Arrangement: R T P The remaining persons are Q and S, to be placed in positions 1 and 5. Condition: P should not be seated adjacent to S. Since P is at position 4, its neighbors are positions 3 (T) and 5. Therefore, S cannot be at position 5. S must be at position 1. Possible arrangement for Case 2: (S, R, T, P, Q). (1 arrangement) Total distinct seating arrangements = 2 + 1 = 3. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (B) 3 Solution Let the five seats be represented as (1, 2, 3, 4, 5) from left to right. Given: R is at the second position from the left end. So, the arrangement is: R . Given: P and T cannot be seated at either end (1 or 5). Thus, P and T must occupy positions 3 and 4 in some order. Case 1: P is at position 3 and T is at position 4. Arrangement: R P T The remaining persons are Q and S, to be placed in positions 1 and 5. Condition: P should not be seated adjacent to S. Since P is at position 3, its neighbors are positions 2 (R) and 4 (T). S can be at position 1 or 5 without being adjacent to P. Possible arrangements for Case 1: (Q, R, P, T, S) and (S, R, P, T, Q). (2 arrangements) Case 2: T is at position 3 and P is at position 4. Arrangement: R T P The remaining persons are Q and S, to be placed in positions 1 and 5. Condition: P should not be seated adjacent to S. Since P is at position 4, its neighbors are positions 3 (T) and 5. Therefore, S cannot be at position 5. S must be at position 1. Possible arrangement for Case 2: (S, R, T, P, Q). (1 arrangement) Total distinct seating arrangements = 2 + 1 = 3.

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