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ExamsJEE AdvancedMaths

The expression E5(n) is defined as Σ (nCk × k⁴) / Σ (nCk × k³), and it simplifies to n / 4. For n ≤ 109, E5(n) is less than 26. Therefore, the smallest value of n that satisfies the condition E5(n) ≥ 26 is one of the following:

  1. 110
  2. 111
  3. 112
  4. 113

Correct answer: 110

Solution

We find the smallest value of n that satisfies E5(n) ≥ 26 by using the given formula and condition, which simplifies to n / 4, and testing values of n until the condition is met.

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