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BITSAT2018MathematicsBinomial TheoremActual

The greatest term in the expansion of 3 1 + 1 3 20 is

Options

  1. A26840 9
  2. B24840 9
  3. C25840 9
  4. DNone of these

Correct answer

C. 25840 9

Step-by-step solution

T r + 1 = 3 · 20 C r 1 3 r and T r = 3 · 20 C r - 1 1 3 r - 1 Now, T r + 1 T r = 20 - r + 1 r 1 3 Since, T r + 1 ≥ T r ⇒ 20 - r + 1 ≥ 3 r ⇒ r ≤ 21 3 + 1 = 21 2 . 73 ⇒ r ≤ 7 . 692 ⇒ r = 7 ∴ The greatest term is T 8 = 3 · C 7 20 1 3 7 = 25840 9

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