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GATE 2021 ME (ME1) – Question 10

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q. The number of distinct seating arrangements possible is:

  1. 4
  2. 8
  3. 10
  4. 16

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Show answer and explanation

Correct answer: (D) 16

Explanation

Q can occupy positions 1,2,3,4,5. The respective valid choices for R and S contribute 4,2,4,2,4 arrangements after the two remaining people are permuted.

For example, with Q at 1, R must be at 3; S may be at 4 or 5, and P,T have two orders. Summing gives **16 (D)**.