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GATE 2021 CY – Question 5

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 1 mark · Multiple choice

Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:

  1. 2
  2. 4
  3. 6
  4. 8

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Show answer and explanation

Correct answer: (C) 6

Explanation

Of 4!=24 arrangements, those with adjacent P/R number 2×3!=12: treat the pair as one block and allow both internal orders.

Thus 12 arrangements have P/R nonadjacent. Exchanging Q and S pairs these arrangements, with exactly one of each pair placing S to the right of Q.

Therefore **12/2=6, C**.