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

Correct answer: A. 1680 (9 !)/((3 ! 3 ! 3 !) 3 !) × 3 !

JEE Main 20245 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 5 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Sets and Relations

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Sets and Relations

Let the set S=\ 2,4,8,16, , 512\ be partitioned into 3 sets A, B, C...

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

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

Options

A1680
B1640
C1520
D1710

Correct answer

A. 1680

Step-by-step solution

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

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

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