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:

Permutations and Combinations: JEE Main 2024 Mathematics question

JEE Main 2024 · 5 Apr, Evening shift · Q4837

JEE Main 20245 Apr, Evening shiftMathematicsMediumPermutations and Combinations98× since 2002

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: