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JEE Main20199 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

If the fourth term in the Binomial expansion of 2 x + x l o g 8 x 6 , x > 0 is 20 × 8 7 , then a value of x is

Options

  1. A8 – 2
  2. B8
  3. C8 3
  4. D8 2

Correct answer

D. 8 2

Step-by-step solution

The general term in the binomial expansion a + b n is T r + 1 = C r n a n - r b r . Given, the fourth term in the expansion of 2 x + x log 8 x 6 is T 4 = 20 × 8 7 ⇒ C 3 6 2 x 3 x log 8 x 3 = 20 × 8 7 ⇒ 6 ! 3 ! · 3 ! 2 x 3 x log 8 x 3 = 20 × 2 3 7 ⇒ 6 × 5 × 4 × 3 ! 3 × 2 × 1 · 3 ! 2 x 3 x log 8 x 3 = 20 × 2 21 ⇒ 20 2 x 3 x log 8 x 3 = 20 × 2 21 ⇒ 2 x x log 8 x 3 = 2 7 3 ⇒ 2 x x log 8 x = 2 7 ⇒ 1 x x log 8 x = 2 6 &#

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