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JEE Main2015MathematicsBinomial TheoremActual

If the coefficient of the three successive terms in the binomial expansion of 1 + x n are in the ratio 1 : 7 : 42 , then the first of these terms in the expansion is

Options

  1. A9 th
  2. B6 th
  3. C8 th
  4. D7 th

Correct answer

D. 7 th

Step-by-step solution

Let coefficient of first term is C r n C r n C r + 1 n = 1 7 ⇒   r + 1 n - r = 1 7 ⇒   7 r + 7 = n - r n - 8 r = 7               … 1 Also, C r + 1 n C r + 2 n = 7 42 = 1 6 ⇒ r + 2 n - r - 1 = 1 6 ⇒ 6 r + 12 = n - r - 1 n - 7 r = 13               … 2 Solving 1 and 2 , we get r = 6 Hence, 7 th term is the answer.

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