Verified Solution • 2025–26 Session moderate

QJEEM24Maa04d: JEE Main 2024 Mathematics - Class 11 JEEM24Maa04d Solution: Let the set be partitioned into 3 sets with equal number of…

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

Multiple Choice Options

  • A 1640
  • B 1520
  • C 1710
  • D 1680

Step-by-Step Verified Solution

Given set S={21,22,…29}S=\left\{2^1, 2^2, \ldots 2^9\right\} which consist of 9 elements.

Maximum number of possible partitions (in set A,BA, B and CC )

=9C3⋅6C3⋅3C3=1680={ }^9 C_3 \cdot{ }^6 C_3 \cdot{ }^3 C_3=1680

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