Let the set S=\ 2,4,8,16, ldots . ., 512\ be partitioned into 3 sets A , B , C with equal number of elements such that A cup B cup C = S and A cap B = B cap C = A cap C =φ . The maximum number of such possible partitions of S is equal to :

Mathematics · Sets and Relations

JEE Main 2024 — 5 April, Shift 2 — Question 13

Let the set $S=\{2,4,8,16, \ldots . ., 512\}$ be partitioned into 3 sets $\mathrm{A}, \mathrm{B}, \mathrm{C}$ with equal number of elements such that

$\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}=\mathrm{S}$ and $\mathrm{A} \cap \mathrm{B}=\mathrm{B} \cap \mathrm{C}=\mathrm{A} \cap \mathrm{C}=\phi$ . The maximum number of such possible partitions of $S$ is

equal to :

Option A:
1680
Correct
Option B:
1520
Option C:
1710
Option D:
1710

Answer: A

Step-by-step solution

$\frac{9!}{(3!3!3!) 3!} \times 3$ !

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 5 April, Shift 2
Subject: Mathematics
Chapter: Sets and Relations
Topic: Sets