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TIFR-2016-Maths-A: 16

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Let $S$ be a collection of subset of $\left \{ 1,2,\dots,100 \right \}$ such that the intersection of any two sets in $S$ is non-empty. What is the maximum possible cardinality $\left | S \right |$ of $S$ ?

  1. $100$
  2. $2^{100}$
  3. $2^{99}$
  4. $2^{98}$
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