GATE 2024 BM – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people.

How many unique seating arrangements are possible such that each person is sitting next to their twin?

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 12

Explanation

Each pair takes two adjacent chairs, so on the 8 chairs we place 3 pairs (blocks of 2) and 2 empty chairs. Tilings of a labelled 8-cycle with 3 blocks and 2 empty chairs number $\frac{8}{5}\binom{5}{3} = 16$. The three pairs are distinct, so there are $16 \times 3! = 96$ placements. Rotations of the table give the same arrangement (8 rotations, each giving a different placement), so there are $96 / 8 = 12$ arrangements.

More Quantitative Aptitude: Algebra, Geometry and Mensuration questions

GATE 2024 BM Q10 – During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun…
GATE 2023 BM Q7 – Which function represents the given graph?
GATE 2022 BM Q3 – If r is a root of x²+2x+6=0, find (r+2)(r+3)(r+4)(r+5).
GATE 2021 BM Q4 – Define operators by p⊙q=p−q and p⊕q=p×q. Evaluate (9⊙(6⊕7))⊙(7⊕(6⊙5)).
GATE 2020 BM Q9 – A 4×4 matrix M=[mᵢⱼ] has zero diagonal and mᵢⱼ=−mⱼᵢ. What minimum number of entries…
GATE 2025 CS (CS1) Q7 – In the diagram, the lines QR and ST are parallel to each other. The shortest distance…

All Quantitative Aptitude: Algebra, Geometry and Mensuration questions →