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JEE Main20198 Apr 2019Evening ShiftMathematicsBinomial TheoremActual

If the fourth term in the binomial expansion of x 1 1 + l o g 10 x + x 1 12 6 is equal to 200 , and x > 1 , then the value of x is

Options

  1. A100
  2. B10 4
  3. C10 3
  4. D10

Correct answer

D. 10

Step-by-step solution

General term for the given binomial is T r + 1 = 6 C r x 1 1 + l o g 10 x 6 - r x 1 12 r Given T 4 = 200 , putting r = 3 ⇒ T 4 = 6 C 3 x 1 1 + l o g 10 x 3 x 1 12 3 = 200 ⇒ x 1 1 + l o g 10 x 3 2 ⋅ x 1 4 = 10 ⇒ x 3 2 1 + l o g 10 x + 1 4 = 10 ⇒ 3 2 1 + l o g 10 x + 1 4 l o g 10 x = 1 ⇒ x = 10 , 10 - 4 ⇒ x = 10 ( as x > 1 )

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