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JEE MainMathematicsBinomial Theorem

In the binomial expansion of (1+x)²⁰ , 8 times the coefficient of the p^ th term is equal to the coefficient of the (p+2)^ th term. The value of p is :

Options

  1. A4
  2. B5
  3. C12
  4. D15

Correct answer

B. 5

Step-by-step solution

8 ²⁰C_ p-1 = ²⁰C_ p+1 8 20! (p-1)!(21-p)! = 20! (p+1)!(19-p)! 8 (21-p)(20-p) = 1 p(p+1) 8p(p+1) = (21-p)(20-p) 8p^2 + 8p = 420 - 41p + p^2 7p^2 + 49p - 420 = 0 p^2 + 7p - 60 = 0 (p+12)(p-5) = 0 Since p must be a positive integer, p = 5 . Answer: 5

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