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NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The value of the numerically greatest term in the expansion of 4 - 3 x 7 when x = 2 3 is equal to

Options

  1. A71680
  2. B35840
  3. C10752
  4. D86016

Correct answer

D. 86016

Step-by-step solution

We know that, T r + 1 has the greatest numerical value where, r = n + 1 a x + a ,   where   . = GIF ⇒ r = 7 + 1 - 3 x - 3 x + 4 = 8 3 ⋅ 2 3 3 2 3 + 4 = 2 ⇒ T 3 will be the term with greatest numerical value and T 3 = 7 C 2 4 5 3 x 2 = 7 C 2 4 5 3 2 2 3 2 = 86016 .

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